Electric Charge - Module 1 PDF

**MODULE 1** **Electric Charge Definition** Electric charge can be defined as a fundamental property of subatomic particles that gives rise to the phenomenon of experiencing force in the presence of electric and magnetic fields. These fields exert influence on charged particles, resulting in obser...

**MODULE 1** **Electric Charge Definition** Electric charge can be defined as a fundamental property of subatomic particles that gives rise to the phenomenon of experiencing force in the presence of electric and magnetic fields. These fields exert influence on charged particles, resulting in observable effects. **Types of Electric Charge** Electric charge comes in two main types: **positive and negative charges**. Positive charges are associated with protons, which are subatomic particles residing in the nucleus of an atom. They are represented by the symbol "+". On the other hand, negative charges are linked to electrons, which orbit the atomic nucleus and are denoted by the symbol "-". The distinction between positive and negative charges plays a vital role in comprehending the behaviour of electrically charged objects. Opposite charges, such as positive and negative, attract each other, while like charges, such as positive and positive or negative and negative, repel each other. This fundamental principle is the foundation for various concepts in electromagnetism and is pivotal in understanding the interaction of charged particles. When an object carries a negative charge, it possesses an excess of electrons compared to protons. Conversely, a positive charge indicates an excess of protons relative to electrons. It's important to note that when an equal number of positive and negative charges are present, they cancel each other out, resulting in a neutral state for the object. By grasping the definition of electric charge and recognizing the significance of positive and negative charges, one can understand the fundamental principles governing electricity and magnetism. **Note:** In the context of electric charge, the terms "attraction" and "repulsion" are used to describe how charges interact with each other. **Is Electric Charge a Vector Quantity?** No, electric charge is not a vector quantity; it is a scalar quantity. While vectors have both magnitude and direction and obey vector addition laws like the triangle law and parallelogram law, electric charge does not exhibit these properties. When currents meet at a junction, the resulting current is determined by the algebraic sum of the individual currents rather than their vector sum. Thus, electric charge is considered a [scalar quantity](https://byjus.com/physics/scalars-and-vectors/), despite having magnitude and direction. **Measuring Electric Charge** Coloumb is the unit of electric charge. "One coulomb is the quantity of charge transferred in one second." Mathematically, the definition of a coloumb is represented as: Q = I.t **In the equation, Q is the electric charge, I is the electric current and t is the time** **Coulomb's Law** We know that like charges repel each other, while unlike charges attract. However, have you ever wondered about the strength of these forces acting between charges? Coulomb's Law offers us a method to calculate this force precisely. According to Coulomb's Law, the magnitude of the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance separating them. The Coulomb's Law is given by the expression: Fe=kq1q2r2 **where F~e~ is the electric force, q~1~ and q~2~ are electric charges, k is the Coulomb's constant 8.988×10^9^ N⋅m^2^/C^2^ and r is the distance of separation.** By applying Coulomb's Law, we can quantitatively determine the strength of the electric force between charges and gain valuable insights into their interactions. This fundamental principle holds great significance in the field of electromagnetism and enables us to analyse various electrical phenomena. Through the application of Coulomb's Law, scientists and researchers have been able to uncover the intricate workings of electric forces and comprehend their profound impact on the world around us. **What is Ampere?** - Ampere is named after the French Physicist and Mathematician Andre-Marie Ampere.  - One ampere of current represents one coulomb of electrical charge, i.e. 6.24×10^18^ charge carriers, moving in one second.  - In other words, "an ampere is the amount of current produced by the force of one volt acting through a resistance of one ohm". - mpere is defined as the unit of electric current that is equal to the flow of one Coulomb per second. - The relationship between ampere and coulomb is represented as follows: - Ampere = 1 Coulomb / Second - At any given point in an area experiencing current, the Ampere value will increase proportionately if the charge on particles moving through it increases. **voltage** **Voltage** is the pressure from an electrical circuit\'s power source that pushes [charged electrons (current)](https://www.fluke.com/en-in/search/fluke/?query=charged+electrons+%28current%29) through a conducting loop, enabling them to do work such as illuminating a light. In brief, **voltage = pressure**, and it is measured in **volts** (V). In electricity\'s early days, voltage was known as **electromotive force** (emf). This is why in equations such as [Ohm\'s Law,](https://www.fluke.com/en-in/learn/blog/electrical/what-is-ohms-law) voltage is represented by the symbol **E**. Example of voltage in a simple direct current (dc) circuit: What is voltage? - Header 1. In this dc circuit, the switch is closed (turned ON). 2. Voltage in the power source---the \"potential difference\" between the battery\'s two poles---is activated, creating pressure that forces electrons to flow as current out the battery\'s negative terminal. 3. Current reaches the light, causing it to glow. 4. Current returns to the power source. Voltage is either **alternating current (ac) voltage** or **direct current (dc) voltage**. Ways they differ: Alternating current voltage (represented on a digital multimeter by ): - Flows in evenly undulating since waves, as shown below:AC voltage - Reverses direction at regular intervals. - Commonly produced by utilities via **generators**, where mechanical energy---rotating motion powered by flowing water, steam, wind or heat---is converted to electrical energy. - More common than dc voltage. Utilities deliver ac voltage to homes and businesses where the majority of devices use ac voltage. - Primary voltage supplies vary by nation. In the United States, for example, it\'s 120 volts. - Some household devices, such as TVs and computers, utilize dc voltage power. They use rectifiers (such as that chunky block in a laptop computer\'s cord) to convert ac voltage and current to dc. Generators convert rotating motion into electricity. The rotary motion is commonly caused by flowing water (hydroelectric power) or steam from water heated by gas, oil, coal or nuclear power. Direct current voltage (represented on a digital multimeter by V line dash and ): - Travels in a straight line, and in one direction only. - Commonly produced by sources of stored energy such as **batteries.** - Sources of dc voltage have positive and negative terminals. Terminals establish polarity in a circuit, and polarity can be used to determine if a circuit is dc or ac. - Commonly used in battery-powered portable equipment (autos, flashlights, cameras). **What is potential difference?** Voltage and the term \"potential difference\" are often used interchangeably. Potential difference might be better defined as the potential energy difference between two points in a circuit. The amount of difference (expressed in volts) determines how much potential energy exists to move electrons from one specific point to another. The quantity identifies how much work, potentially, can be done through the circuit. A household AA alkaline battery, for example, offers 1.5 V. Typical household electrical outlets offer 120 V. The greater the voltage in a circuit, the greater its ability to \"push\" more electrons and do work. Voltage/potential difference can be compared to water stored in a tank. The larger the tank, and the greater its height (and thus its potential velocity), the greater the water\'s capacity to create an impact when a valve is opened and the water (like electrons) can flow. Difference Between Work and Energy **DefinitionWork** is the transfer of energy that occurs when a force is applied to an object, which causes it to move in the direction of the force. **Energy is the ability** to do work.Significance It is a measure of the amount of energy transferred to or from an object due to the application of a force over a certain distance. It is a fundamental concept in physics that describes the potential or ability of an object or system to perform actions or undergo transformations. **Scalar or Vector** Work is a scalar quantity, meaning it has magnitude but no specific direction.Energy is a vector quantity, which means it has a magnitude as well as a direction. **Units** The SI unit of work is the joule (J), which is the amount of work done when a force of one newton is applied over a displacement of one meter. The SI unit of energy is also the joule (J), which is equivalent to the work done by one Newton force over a one-meter displacement. **Conservation** Work is not conserved. It is a measure of the transfer of energy from one system to another. Energy is conserved (for a closed system) according to the law of conservation of energy. It can neither be created nor destroyed, but it can be converted from one form to another. **Active Component** An electric circuit element which can supply electric power to the circuit or power gain in the circuit, is known as an **active element** or **active component.** Some common examples of active circuit elements are energy sources (voltage sources or current sources), generators or alternators, semiconductor devices such as transistors, photodiodes, etc. The active elements are the circuit component which are entirely responsible for the flow of electric current in the circuit. **Passive Component** The circuit element which can only absorb electrical energy and dissipates it in the form of heat or stores in either magnetic field or electric field is known as **passive circuit component** or **simply passive component.** Therefore, a passive component cannot provide electric power or power amplification in an electric circuit. Some common examples of passive circuit components are resistor, inductor, capacitor and transformer, etc. sl no **Basis of Difference** **Active Component** **Passive Component** ------- ------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1 Definition A circuit component which can deliver power or power gain in an electric circuit for infinite duration of time is known as active component. A circuit element which only absorbs the power and convert it in heat or stores in electric field or magnetic field is known as passive component. 2 Examples The common examples of active components are energy sources (voltage or current source), generators, semiconductor devices like transistors, solar cells, SCR, etc. The examples of passive components are resistor, inductor, capacitor and transformer, etc. 3 Role in the circuit Active components behave as source of power in the circuit. The passive components act as load in the circuit. 4 Power gain Active components can provide power gain in the electric circuit. Passive components cannot provide power gain. 5 Function Active components receive energy in the forms such as thermal energy, chemical energy, hydraulic energy, etc. and delivers in the circuit in the form of electrical energy. Passive components receive electrical energy and either convert it in the other forms such as heat, light, rotation, etc. or store in the magnetic field or electric field. 6 Power deliver or absorb Active components can deliver as well as absorb the electrical power. For example, a battery, during charging absorbs electrical energy and during discharging delivers electrical energy. A passive element can only absorb electrical power. It is not capable for deliver power. 7 Need of external power source to function Some active components require an external power source to function. For example, the active components like transistors and SCR use electrical energy to function, i.e., to control the power in the circuit. Passive components do not require any external power source to function. The passive components such as resistor, inductor, capacitor, etc. do not require any source of electricity to function, they use some other property to control the power in the circuit 8 Amplification Active components have power gain more than unity, so they can amplify a signal. For passive components, the power gain is less than unity, hence they cannot amplify a signal. Passive Components 1. Resisters **Characteristics of a series circuit** --------------------------------------- In a series circuit, the same amount of current flows through all components. This helps in distributing the current flow accordingly and the connection within this circuit is strong in nature. In a series electrical circuit, all the components are arranged in a single line. The current flow in a series circuit is the same for all lines. The voltage across all other resistors is different in nature. The formula for calculating a total series resistor is Vt=V1+V2+V3 **Characteristics of a parallel circuit** Each of the components is connected to each other with a flowing current. Through the main source of current, this connection is made. A parallel circuit is also known as an electrical circuit.  **Figure 3: Structure of resistors** A parallel circuit is developed by arranging and connecting more than one component, in case of failure of one of its components, the other parts remain connected. The polarities of a parallel circuit are the same in nature.This is a big advantage of using a parallel circuit. Each part of this type of circuit has an individual and independent circuit. The formula for calculating a parallel circuit is Vt=V1=V2=V3. Problem 1   Capacitors in Parallel **Capacitanc**e The total Capacitance of the circuit is the equivalent to the sum of the individual capacitances of the capacitors in the network. CT=C1+C2+C3 Where C~1~ is the capacitance across the 1^st^ capacitor, C~2~ is the capacitance across the 2^nd^ capacitor and C~3~ is the capacitance across the 3^rd^ capacitor in the above network. **Voltage** The voltage measured at the end of the circuit is **same** as the voltage across all the capacitors that are connected in a parallel circuit. VT=V1=V2=V3 Where V~c1~ is the voltage across the 1^st^ capacitor, V~c2~ is the voltage across the 2^nd^ capacitor and V~c3~ is the voltage across the 3^rd^ capacitor in the above network. **Current** The total current flowing is equal to the sum of the currents flowing through each capacitor connected in the parallel network. IT=I1+I2+I3 Where I~1~ is the current through the 1^st^ capacitor, I~2~ is the current through the 2^nd^ capacitor and I~3~ is the current through the 3^rd^ capacitor in the above network. Parallel circuits are wired such that all wires between two points lead to each component, with all components joined by conducting wire. It means the capacitor\'s first and second plates are, respectively **Working of Capacitors in Parallel** When two or more capacitors are connected in parallel, it means we want to increase the storage capacity of the circuit. Their individual capacitance value remains unchanged, while their equivalent capacitance value is calculated using a formula involving all of their values. Let\'s imagine two capacitors C~1~ and C~2~ are connected in a parallel circuit and the charge Q is divided into Q~1~ and Q~2~ that respectively flow from C~1~ and C~2~ So, the Total charge between a and b is Q=Q1+Q2Q=Q1+Q2 Q=C1V+C2VQ=C1V+C2V Q/V=C1+C2Q/V=C1+C2 C=C1+C2 When we add lots of capacitor in parallel than CT=C1+C2+C3+C4..........+Cn Example Let's say we have three capacitors; each one has a capacitance of 50 nF. They are then connected in parallel with the 200 supply. Calculate the Equivalent capacitance **Solution:** C1=C2=C3=50×10−9F Total capacitance in parallel CT=C1+C2+C3+C4..........+Cn CT=(50+50+50)×10−9 CT=150nF Advantages of using Capacitors in Parallel - A capacitor is a passive electronic component that can store energy and deliver it on demand. When we connected capacitors in parallel, it increases the storage capacity of the circuit. - When connected to an alternating current, a capacitor resists changes in voltage and has several electrical properties that make it useful as part of an electronics circuit. - These include its ability to block DC (direct current) while allowing AC (alternating current) signals to pass through. The first thing is simply that, when capacitors are connected in parallel with each other, their voltage decreases proportionally. - Connecting capacitors in parallel help to reduce the number of resistors that are used in the system Disadvantages of using Capacitors in Parallel - For example, a parallel combination of two 0.1 μFμF capacitors has an equivalent capacitance of 0.2 μFμF because both capacitors will share a voltage drop (Voltage division) of 1 V for every doubling of their total capacitance. If one capacitor is accidentally allowed to discharge through another, there could be more than 4 A transient current through one capacitor if it is charged and discharged quickly. This type of current flow may result in severe damage to either or both units and should be avoided at all costs by not paralleling such components without careful consideration. - We know that capacitors in parallel is storing a huge amount of energy but they release this energy in a very short span of time. So, this can be caused heavy injuries or damage to the electrical wiring. Because of that reason, it is not used in the industry materials. **capacitors in Series** ------------------------ Let us observe what happens, when few Capacitors are connected in Series. Let us consider three capacitors with different values, as shown in the figure below. Series Capacitors ### **Capacitance** When the capacitance of a network whose capacitors are in series is considered, the reciprocal of the capacitances of all capacitors, is added to get the reciprocal of the total capacitance. To get this more clearly, The total potential difference across combination is: V = V~1~ + V~2~ V=QC1+QC2 V/Q=C1+C2 The ratio Q/V is called the equivalent capacitance C between points a and b. The equivalent capacitance C is given by: 1/C=1/C1+1/C2 **Important Points:** - If N identical capacitors of capacitance C are connected in series, then effective capacitance = C/N - If N identical capacitors of capacitance C are connected in parallel, then effective capacitance = CN Where C~1~ is the capacitance across the 1^st^ capacitor, C~2~ is the capacitance across the 2^nd^ capacitor and C~3~ is the capacitance across the 3^rd^ capacitor in the above network. ### **Voltage** The voltage across each capacitor depends upon the value of individual capacitances. Which means VC1=QTC1 VC2=QTC2 VC3=QTC3 The total voltage across the series capacitors circuit, VT=VC1+VC2+VC3 Where V~c1~ is the voltage across the 1^st^ capacitor, V~c2~ is the voltage across the 2^nd^ capacitor and V~c3~ is the voltage across the 3^rd^ capacitor in the above network. ### **Current** The total amount of Current that flows through a set of Capacitors connected in series is the same at all the points. Therefore the capacitors will store the same amount of charge regardless of their capacitance value. Current through the network, I=I1=I2=I3 Where I~1~ is the current through the 1^st^ capacitor, I~2~ is the current through the 2^nd^ capacitor and I~3~ is the current through the 3^rd^ capacitor in the above network. As the current is same, the storage of charge is same because any plate of a capacitor gets its charge from the adjacent capacitor and hence capacitors in series will have the same charge. QT=Q1=Q2=Q3 The circuit includes three capacitors. A zero point three zero microfarad capacitor and a ten microfarad capacitor are connected in series, and together they are connected in parallel with a two point five microfarad capacitor. **Inductor** According to the Faraday's law of Electromagnetic induction, When the current flowing through an inductor changes, the time-varying magnetic field induces a voltage in the conductor. According to lens law, the direction of induced EMF opposes the change in current that created it. Hence, **induced EMF is opposite to the voltage** applied across the coil. This is the property of an inductor. The rate of change of current produces change in the magnetic field, which induces an EMF in opposite direction to the voltage source. This property of induction of EMF is called as the **Inductance**. The formula for inductance is Inductance=volatgerateofchangeofcurrentInductance=volatgerateofchangeofcurrent **Units −** - The unit of Inductance is **Henry**. It is indicated by **L**. - The inductors are mostly available in mH milliHenrymilliHenry and μH microHenrymicroHenry. A coil is said to have an inductance of **one Henry** when an EMF of **one volt** is self-induced in the coil where the current flowing changed at a rate of **one ampere per second**. **Self-Inductance** If a coil is considered in which some current flows, it has some magnetic field, perpendicular to the current flow. When this current keeps on varying, the magnetic field also changes and this changing magnetic field, induces an EMF, opposite to the source voltage. This opposing EMF produced is the **self-induced voltage** and this method is called as **self-inductance**. Self Inductance The current **i~s~** in the figure indicate the source current while **i~ind~** indicates the induced current. The flux represents the magnetic flux created around the coil. With the application of voltage, the current **i~s~** flows and flux gets created. When the current **i~s~** varies, the flux gets varied producing **i~ind~**. This induced EMF across the coil is proportional to the rate of change in current. The higher the rate of change in current the higher the value of EMF induced. We can write the above equation as E α dI/dt E=L dI/dt Where, - **E** is the EMF produced - **dI/dt** indicates the rate of change of current - **L** indicates the co-efficient of inductance. Self-inductance or Co-efficient of Self-inductance can be termed as L=E dI/dt The actual equation is written as E=−LdIdt The minus in the above equation indicates that **the EMF is induced in opposite direction to the voltage source** according to Lenz's law. **Mutual Inductance** As the current carrying coil produces some magnetic field around it, if another coil is brought near this coil, such that it is in the magnetic flux region of the primary, then the varying magnetic flux induces an EMF in the second coil. If this first coil is called as **Primary coil**, the second one can be called as a **Secondary coil**. When the EMF is induced in the secondary coil due to the varying magnetic field of the primary coil, then such phenomenon is called as the **Mutual Inductance**.  The current **i~s~** in the figure indicate the source current while **i~ind~** indicates the induced current. The flux represents the magnetic flux created around the coil. This spreads to the secondary coil also. With the application of voltage, the current **i~s~** flows and flux gets created. When the current **i~s~** varies, the flux gets varied producing **i~ind~** in the secondary coil, due to the Mutual inductance property. The change took place like this. VpIp→B→VsIs Where, - ***V~p~*** ***i~p~*** Indicate the Voltage and current in Primary coil respectively - **B** Indicates Magnetic flux - ***V~s~*** ***i~s~*** Indicate the Voltage and current in Secondary coil respectively Mutual inductance **M** of the two circuits describes the amount of the voltage in the secondary induced by the changes in the current of the primary. V(Secondary)=−MΔI/Δt Where ΔI/Δt the rate of change of current with time and **M** is the co-efficient of Mutual inductance. The minus sign indicates the direction of current being opposite to the source. **Units −** The units of Mutual inductance is volt=Mampssec Fromtheaboveequation M=volt.secamp =Henry(H) Depending upon the number of turns of the primary and the secondary coils, the magnetic flux linkage and the amount of induced EMF varies. The number of turns in primary is denoted by N1 and secondary by N2. The co-efficient of coupling is the term that specifies the mutual inductance of the two coils. **Factors affecting Inductance** There are a few factors that affect the performance of an inductor. The major ones are discussed below. **Length of the coil** The length of the inductor coil is inversely proportional to the inductance of the coil. If the length of the coil is more, the inductance offered by that inductor gets less and vice versa. **Cross sectional area of the coil** The cross sectional area of the coil is directly proportional to the inductance of the coil. The higher the area of the coil, the higher the inductance will be. **Number of turns** With the number of turns, the coil affects the inductance directly. The value of inductance gets square to the number of turns the coil has. Hence the higher the number of turns, square of it will be the value of inductance of the coil. **Permeability of the core** The **permeability **μ of the core material of inductor indicates the support the core provides for the formation of a magnetic field within itself. The **higher** the permeability of the core material, the **higher** will be the inductance. **Coefficient of Coupling** This is an important factor to be known for calculating Mutual inductance of two coils. Let us consider two nearby coils of N1 and N2 turns respectively. The current through first coil i~1~ produces some flux Ψ~1~. The amount of magnetic flux linkages is understood by weber-turns. Let the amount of magnetic flux linkage to the second coil, due to unit current of i~1~ be N2φ1i1 This can be understood as the Co-efficient of Mutual inductance, which means M=N2φ1i1 Hence the Co-efficient of Mutual inductance between two coils or circuits is understood as the weber-turns in one coil due to 1A of current in the other coil. If the self-inductance of first coil is L~1~, then L1i1=N1φ1=\>L1N1φ1i1 M=N2L1N1 Similarly, coefficient of mutual inductance due to current i~2~ in the second coil is M=N1φ2i2⋯⋯⋯⋯1 If self-inductance of second coil is L~2~ L2i2=N2φ2 L2N2=φ2i2 Therefore, M=N1L2N2⋯⋯⋯⋯2 Multiplying 1 and 2, we get M×M=N2L1N1×N1L2N2 M2=L1L2=\>M=L1L2−−−−√ The above equation holds true when the whole changing flux of primary coil links with the secondary coil, which is an ideal case. But in practice, it is not the case. Hence, we can write as M≠L1L2−−−−√M≠L1L2 andML1L2−−−−√=K≠1andML1L2=K≠1 Where K is known as the coefficient of coupling. The **Coefficient of coupling K** can be defined as the ratio of actual coefficient of mutual inductance to the ideal maximum coefficient of mutual inductance. If the value of k is near to unity, then the coils are said to be tightly coupled and if the value of k = 0, then the coils are said to be loosely coupled. **Inductors in Series** Let us observe what happens, when few inductors are connected in Series. Let us consider three resistors with different values, as shown in the figure below. Inductors in Series **Inductance** The total inductance of a circuit having series inductors is equal to the sum of the individual inductances. Total inductance value of the network given above is LT=L1+L2+L3 Where L~1~ is the inductance of 1^st^ resistor, L~2~ is the inductance of 2^nd^ resistor and L~3~ is the inductance of 3^rd^ resistor in the above network. **Voltage** The total voltage that appears across a series inductors network is the addition of voltage drops at each individual inductances. Total voltage that appears across the circuit V=V1+V2+V3 Where V~1~ is the voltage drop across 1^st^ inductor, V~2~ is the voltage drop across 2^nd^ inductor and V~3~ is the voltage drop across 3^rd^ inductor in the above network. **Current** The total amount of Current that flows through a set of inductors connected in series is the same at all the points throughout the network. The Current through the network I=I1=I2=I3 Where I~1~ is the current through the 1^st^ inductor, I~2~ is the current through the 2^nd^ inductor and I~3~ is the current through the 3^rd^ inductor in the above network. **Inductors in Parallel** Let us observe what happens, when few resistors are connected in Parallel. Let us consider three resistors with different values, as shown in the figure below.  **Inductan**ce The total inductance of a circuit having Parallel resistors is calculated differently from the series inductor network method. Here, the reciprocal 1/R1/R value of individual inductances are added with the inverse of algebraic sum to get the total inductance value. Total inductance value of the network is LT=L1+L2+L3 Where L~1~ is the inductance of 1^st^ inductor, L~2~ is the inductance of 2^nd^ inductor and L~3~ is the inductance of 3^rd^ inductor in the above network. From the method we have for calculating parallel inductance, we can derive a simple equation for two-inductor parallel network. It is LT=L1×L2L1+L2 **Voltage** The total voltage that appears across a Parallel inductors network is same as the voltage drops at each individual inductances. The Voltage that appears across the circuit V=V1=V2=V3 Where V~1~ is the voltage drop across 1^st^ inductor, V~2~ is the voltage drop across 2^nd^ inductor and V~3~ is the voltage drop across 3^rd^ inductor in the above network. Hence the voltage is same at all the points of a parallel inductor network. **Current** The total amount of current entering a Parallel inductive network is the sum of all individual currents flowing in all the Parallel branches. The inductance value of each branch determines the value of current that flows through it. The total Current through the network is I=I1+I2+I3 Where I~1~ is the current through the 1^st^ inductor, I~2~ is the current through the 2^nd^ inductor and I~3~ is the current through the 3^rd^ inductor in the above network. Hence the sum of individual currents in different branches obtain the total current in a parallel network. **Inductive Reactance** Inductive Reactance is the opposition offered by an inductor to the alternating current flow, or simply AC current. An inductor has the property of resisting the change in the flow of current and hence it shows some opposition which can be termed as **reactance**, as the frequency of the input current should also be considered along with the resistance it offers. - Indication − **XL** - Units − **Ohms** - Symbol − **Ω** In a purely inductive circuit, the current **I~L~ lags** the applied voltage by 90°. Inductive reactance is calculated by, XL=2πfL Where f is the frequency of the signal. Hence inductive reactance is a function of frequency and inductance. **Kirchhoff\'s Laws** Kirchhoff\'s Laws quantify how current flows through a circuit and how voltage varies around a loop in a circuit. - Kirchhoff\'s current law (1st Law) states that the current flowing into a node (or a junction) must be equal to the current flowing out of it. This is a consequence of charge conservation. - Kirchhoff\'s voltage law (2nd Law) states that in any complete loop within a circuit, the sum of all voltages across components which supply electrical energy (such as cells or generators) must equal the sum of all voltages across the other components in the same loop. This law is a consequence of both charge conservation and the conservation of energy. **[Kirchhoff\'s Current Law]** Current flow in circuits occurs when charge carriers travel around the circuit. Current is defined as the rate at which this charge passes any point in the circuit. A fundamental concept in physics is that charge will always be conserved. In the context of circuits this means that, since current is the rate of flow of charge, the current flowing into a point must be the same as current flowing out of that point. Figure 1: Three wires connected at a node with different currents travelling down each wire. Kirchhoff\'s current law states that for the node in Figure 1, the currents in the three wires must be related by:*I*1​+*I*2​=*I*3​It is important to note what is meant by the signs of the current in the diagram - a positive current means that the currents are flowing in the directions indicated on the diagram. Directions are the direction in which any positive charges would flow, that is from the + of the battery round the circuit to the −. The standard way of displaying Kirchhoff\'s current law is by having all currents either flowing towards or away from the node, as shown in Figure 2:  Figure 2: The same node as in Figure 1, but with the currents defined to be pointing inward. The values *I*1​,*I*2​,*I*3​ can be positive or negative. Here, at least one of the currents will have a negative value (in the opposite direction to the arrows on this diagram) and Kirchhoff\'s current law here would be written as:*I*1​+*I*2​+*I*3​=0This can be generalised to the case with *n* wires all connected at a node by writing:*k*=1∑*n*​*Ik*​=0 **Problem find** current I **Kirchhoff\'s voltage law ** As charge carriers flowing through a circuit pass though a component, they either gain or lose electrical energy, depending upon the component (cell or resistor, for example). This is due to the fact that [work](https://isaacphysics.org/concepts/cp_work) is done on or by them as a result of the electric forces inside the components. The total work done on a charge carrier by electric forces in supply components (such as cells) must equal the total work done by the charge carrier in other components (such as resistors and lamps) by the time it has gone round the circuit once. This means that the sum of all potential differences across the components involved in a circuit\'s loop must be zero if we count voltages across supply components as positive and across \'electricity using\' components as negative.  **Figure 4:** The overall voltage gain (or loss) around the loop shown is zero. **Figure 4** gives an example of this. Let us start at the − terminal of the battery, and label the potential (or voltage) of this point 0V. We go around the circuit in the direction of the arrow, which is the direction in which we think current will flow. On passing the battery, the potential increases by 6V to 6V. We then lose 4V on passing the 2Ω resistor to give a new potential of 2V. Finally, the potential drops by 2V in the 1Ω resistor back to zero again. Kirchhoff\'s voltage law can be summarised in this situation as6 V−4 V−2 V=0 6 V−(2 A×2 Ω)−(2 A×1 Ω)=0  **Step 1:** The first and foremost step is to draw a closed loop to a circuit. Once done with it, draw the direction of the flow of current. **Step 2:** Defining our sign convention is very important\ Sign Convention **Step 3:** Using Kirchhoff's first law, at B and A we get, **I~1~+I~2~=I~3~** **Step 4:** By making use of the above convention and Kirchhoff's Second Law, **From Loop 1 we have:** 10=R1∗I1+R3∗I3 =10I1+40I3 1=I1+4I3 **From Loop 2 we have :** 20=R2∗I2+R3∗I3 20I2+40I3 1=I2+2I3 **From Loop 3 we have :** 10−20=10I1−20I2 1=−I1+2I2 By making use of Kirchhoff's First law, **I~1~+I~2~=I~3~** Equation reduces as follows (from Loop 1 ) : 1=5I1+4I2 Equation reduces as follows ( from Loop 2 ) : 1=2I1+3I2 This results in the following Equation: I1=−13I2 From last three equations we get, 1=13I2+2I2 I2=0.429A I1=0.143A I3=0.286A [**Electric circuits**](https://www.tutorialspoint.com/electronic_circuits/index.htm) are classified into two main types namely **series circuit** and **parallel circuit** based on the arrangement of components in the circuit. A series circuit is one in which the components are chain connected, while a parallel circuit is one in which all the circuit components are connected between two common points. Series circuits and parallel circuits act as voltage divider circuits and current divider circuits, respectively. Read through this article to find out more about Current Division Rule and Voltage Division Rule. Current Division Rule A parallel circuit acts as a **current divider** as it divides the total circuit current in its all branches. Figure1 shows a current divider circuit in which the total circuit current *I* has been divided into currents *I~1~* and *I~2~* in two parallel branches with resistances *R~1~* and *R~2~*. Although, we can notice that the voltage drop across both resistances is same, i.e., *V*.  According to Ohm's law, I1=V/R1 and I2=V/R2 Let R is the equivalent resistance of the circuit, and it is given by, R=R1R2 / R1+R2⋅⋅⋅(1) Also, from the circuit, we get, I=V/R= V×(R1+R2R1R2)⋅⋅⋅(2) But, we know that the voltage across both resistances is same. ∴V=I1R1=I2R2⋅⋅⋅(3) Hence, from equations (2) & (3), we finally get, I=I1R1 (R1+R2/ R1R2) =I1 (R1+R2)/R2) ∴I1=IR2 / R1+R2⋅⋅⋅(4) Similarly, I=I2R2(R1+R2/R1R2)=I2(R1+R2/R1) ∴I2=IR1 /(R1+R2)⋅⋅⋅(5) Equations (4) and (5) give the expressions of current division rule. From these equations, we may state that the current in any of the parallel branches is equal to the ratio of opposite branch resistance to the sum of all resistances, multiplied by the total circuit current. **Voltage Division Rule** A series circuit acts as a **voltage divider** as it divides the total supply voltage into different voltages across the circuit elements. Figure2 shows a voltage divider circuit in which the total supply voltage *V* has been divided into voltages *V~1~* and *V~2~* across two resistances *R~1~* and *R~2~*. Although, the current through both resistances is same, i.e., *I*. According to Ohm's law, V1=IR1andV2=IR2V1=IR1andV2=IR2 Let *R* is the total resistance of the circuit, and it is given by, R=R1+R2⋅⋅⋅(1) Also, from the circuit, we have, V=IR=I(R1+R2)⋅⋅⋅(2) But I=V1R1=V2R2⋅⋅⋅(3) Therefore, from equations (2) & (3), we finally get, V=V1R1(R1+R2) ∴V1=VR1R1+R2⋅⋅⋅(4) Similarly, V=V2R2 / (R1+R2) ∴V2=VR2 / R1+R2⋅⋅⋅(5) Hence, from equations of voltage division rule, it may be said that the voltage across a resistor in a series circuit is equal to the product of the value of that resistor and the total supply voltage, divided by the total resistance of the series resistors. Explore our **latest online courses** and learn new skills at your own pace. Enroll and become a certified expert to boost your career. Numerical Example (1) Find the currents *I~1~* and *I~2~* in the parallel circuit shown in Figure3  Solution Using the current division rule, the current through resistor *R~1~* is, I1=I×R2/R1+R2=20×10/5+10I ∴I1=13.33A The current through resistor *R~2~* will be, I2=I×R1R1+R2=20×55+10I ∴I2=6.67A Numerical Example (2) Find the voltage across resistors *R~1~* and *R~2~* in the circuit shown in Figure-4. Solution Using the voltage division rule, the voltage across resistor R~1~ will be, V1=VR1 / R1+R2=12×6 /6+10=4.5V The voltage across the resistor R~2~ will be, V2=VR2 / R1+R2=12×10 / 6+10=7.5V Summary The following points summarize what we discussed in this article − - A parallel circuit acts as a current divider circuit because it divides the total circuit current in its all branches. - A series circuit acts as a voltage divider circuit because it divides the total supply voltage in different voltages across various component of the circuit. - The current division rule states that the current in any of the parallel branches of a parallel circuit is equal to the ratio of opposite branch resistance to the sum of all resistances, multiplied by the total current. - The voltage division rule states that the voltage across any of the series components in a series circuit is equal to the product of value of that resistance and the total supply voltage, divided by the total resistance of the series circuit.