Electrical Circuit PDF

Electrical Circuit  Charge and Current Charge: Charge is an electrical property of the atomic particles of a matter. S.I Unit: Coulomb (C) Symbol: Q Current: Rate of change of charge. OR Continuous flow of ele...

Electrical Circuit  Charge and Current Charge: Charge is an electrical property of the atomic particles of a matter. S.I Unit: Coulomb (C) Symbol: Q Current: Rate of change of charge. OR Continuous flow of electrons in an electrical circuit. S.I Unit: Ampere (A) Symbol: I  Charge and Current Mathematically, 𝑡 𝑑𝑄 𝐼= 𝑜𝑟 𝑄 = ∫ 𝐼. 𝑑𝑡 𝑑𝑡 𝑡0 Or, in simple terms: 𝑄 𝐼= 𝑇 So, 1 Ampere = 1 coulomb/ 1 second.  QUICK QUIZ (Poll 1) 1 Coulomb is same as: A. Watt /sec B. Ampere/sec C. Joule-sec D. Ampere-sec  QUICK QUIZ (Poll 2) The total charge entering the terminal is 5𝑠𝑖𝑛4𝜋𝑡 𝑚𝐶. Calculate current at t= 0.5 sec.: A. 31.2 A B. 31.2 mA C. 62.8 mA D. 62.8 A  QUICK QUIZ (Poll 2) The total charge entering the terminal is 5𝑠𝑖𝑛4𝜋𝑡 𝑚𝐶. Calculate current at t= 0.5 sec.: 5x4pixcos(4pit) mC A. 31.2 A 5x4pixcos(4pi/2) mC B. 31.2 mA 5x4pi mC C. 62.8 mA 62.8 mC D. 62.8 A  Voltage is the force that moves the electrons in the circuit. The unit for measuring voltage is the volt (V). One volt is equal to current of 1 amp times resistance of 1 ohm. 1V = 1A * 1Ω  Electric Power The electric power P is equal to the energy consumption E divided by the consumption time t: Example Find the electric power of an electrical circuit that consumes 120 joules for 20 seconds. Electric power calculation  Network Components Active Passive Battery Resistance (R) Capacitance (C) Transistor, Inductance (L) Op-amp, Diode  Resistance 1) It is opposition to the flow of current. 2) Resistance (R) is measured in ohms. 3) One ohm is the resistance of a circuit or circuit element that permits a steady current flow of one ampere when one volt is applied to the circuit. 4) Resistors are the components manufactured to possess a specific value of resistance to the flow of current. 1) Series circuit: RT = R1 + R2 + R3 … + Rn 2) Parallel circuit: 1/RT = 1/R1 + 1/R2 + 1/R3 … + 1/Rn  CAPACITANCE Capacitance a)Capacitance is the ability of a body to store an electrical charge. Q = CV Capacitor a) Possesses a specific amount of capacitance Capacitors Total capacitance in series circuits: Total capacitance in parallel circuits: INDUCTANCE INDUCTANCE It exhibits the property of storing energy in a magnetic field. v=L*di/dt Represented by the letter L ⚫ HENRY (H) Unit for measuring inductance ⚫ INDUCTOR Designed to have a specific inductance. INDUCTORS (CONT’D.) Total inductance in series circuits: Total inductance in parallel circuits:  Ohm’s Law Ohm’s law states that: “the current in an electric circuit is directly proportional to the voltage across its terminals, provided that the physical parameters like temperature, etc. remain constant” Mathematically, 𝐼α𝑉 Or, 𝑉 𝐼= 𝑅 𝑙 Where, Resistance 𝑅 = ρ 𝐴 Resistivity Table The resistivity of a conductor is the resistance that a material offers per unit length for a unit cross-section. It's an intrinsic property of the material that measures how well it resists the flow of current. The symbol for resistivity is ρ, and its SI unit is ohm-meters (Ωm)  Conductance A useful quantity in circuit analysis is the reciprocal of resistance R, known as conductance and denoted by G 1 𝐼 𝐺= = 𝑅 𝑉 S.I Unit: mho (ohm spelled backwards) or Siemens Symbol:  Power dissipated in the resistor can be expressed as: 2 𝑉 𝑃 = 𝑉𝐼 = 𝐼2 𝑅 = 𝑅  Applications of Ohm’s Law 1. To find unknown Voltage (V) 2. To Find unknown Resistance (R) 3. To Find unknown Current (I) 4. Can be used to find Unknown Conductance (G)=1/R 5. Can be used to find unknown Power (P)=VI  Applications of Ohm’s Law 1. It is widely used in circuit analysis. 2. It is used in ammeter, multimeter, etc. 3. It is used to get the desired circuit drop in circuit design. 4. Advanced laws such as Norton’s law, Thevenin’s law are based on ohm’s law. 5. A laptop and mobile charger using DC power supply in operation and working principle of DC power supply depend on ohm’s law.  Limitations of Ohm’s Law Ohm’s law holds true only for a conductor at a constant temperature. Resistivity changes with temperature. Ohm’s law by itself is not sufficient to analyze circuits. It is NOT applicable to non linear elements, For example, Diodes, Transistors etc.  QUICK QUIZ (Poll 7) The voltage and the conductance of the given circuit is: A. 30 V, 10 µS B. 30 mV, 100 µS C. 30 V, 100 µS D. 30 mV, 10 µS  QUICK QUIZ (Poll 7) The voltage and the conductance of the given circuit is: A. 30 V, 10 µS B. 30 mV, 100 µS C. 30 V, 100 µS D. 30 mV, 10 µS V=IR= 3mAX10Kohm=30 volts G=1/R= 1/10^4= 100 uS  QUICK QUIZ (Poll 8) The power of the given circuit is: A. 60 mW B. 70 mW C. 80 mW D. 90 mW  QUICK QUIZ (Poll 8) The power of the given circuit is: A. 60 mW B. 70 mW C. 80 mW P=I^2R D. 90 mW =(3mA)^2X10Kohm 90 mW  Series Connection SERIES CONNECTION: Two or more elements are in series if they exclusively share a single node and consequently carry the same current. 100 amps for one hour. Point to Remember for Series Circuits  Parallel Connection PARALLEL CONNECTION: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them Note: Resistors in series behave as a single resistor whose resistance is equal to the sum of the resistances of the individual resistors. Resistors in Parallel. How to find Equivalent Resistance for Series-Parallel Combinations Example: To find 𝑹𝒆𝒒  QUICK QUIZ (Poll 9) Find Equivalent Resistance in Ohms? A. 5 B. 10 C. 15 D. 20  QUICK QUIZ (Poll 9) Find Equivalent Resistance in Ohms? A. 5 B. 10 C. 15 D. 20 Series-12 ohm Parallel- 4 and 12 ohm Series- 3 ohm and 3 ohm Parallel- 6 ohm and 6 ohm Series- 4 ohm, 3 ohm, 3 ohm= 10 ohm  Kirchhoff’s Law Ohm’s law by itself is not sufficient to analyze circuits. However, when it is coupled with Kirchhoff’s two laws, we have a sufficient, powerful set of tools for analyzing a large variety of electric circuits. These laws are: 1. Kirchhoff’s Current Law (KCL) 2. Kirchhoff’s Voltage Law (KVL)  Kirchhoff’s Current Law (KCL) It states that: “the algebraic sum of currents entering/leaving a node is zero”. OR “ Sum of currents entering a node = Sum of currents leaving a node “ Based on Law of Conservation of Charge. Mathematically, ∑ 𝐼 = 0  QUICK QUIZ (Poll 1) KCL equation for the given network is: A. 𝐼1 + 𝐼2 + 𝐼3 B. 𝐼1 + 𝐼2 − 𝐼3 C. 𝐼1 − 𝐼2 + 𝐼3 D. -𝐼1 − 𝐼2 + 𝐼3  Kirchhoff’s Voltage Law (KVL) It states that: “algebraic sum of all voltages around a closed path (or loop) is zero.” OR “ Sum of voltage drops = Sum of voltage rises.” Based on Law of Conservation of Energy Mathematically, ∑ 𝑉 = 0  Kirchhoff’s Voltage Law Kirchhoff’s voltage law states that the algebraic sum of the voltage in any loop must be equal to zero as: ΣV = 0. Restated: The sum of all the voltage drops in a closed circuit will equal the voltage source. Since the two resistors, R1 and R2 are wired together in a series connection, they are both part of the same loop so the same current must flow through each resistor. Thus the voltage drop across resistor, R1 is I*R1 and the voltage drop across resistor, R2 is I*R2 giving by KVL: Finding the voltage drop across the resistors  Kirchhoff’s Current Law The algebraic sum of all the currents entering and leaving a junction is equal to zero Restated: Total current into a junction is equal to the total current out of the junction  QUICK QUIZ (Poll 1) KCL equation for the given network is: A. 𝐼1 + 𝐼2 + 𝐼3 B. 𝐼1 + 𝐼2 − 𝐼3 C. 𝐼1 − 𝐼2 + 𝐼3 D. -𝐼1 − 𝐼2 + 𝐼3 Voltage Q: Three resistors of values: 10 ohms, 20 ohms and 30 ohms, respectively are connected in series across a 12 volt battery supply. Calculate: a) total resistance, b) total circuit current, c) current through each resistor, d) the voltage drop across each resistor, e) verify that Kirchhoff’s voltage law, KVL holds true. Q: Three resistors of values: 10 ohms, 20 ohms and 30 ohms, respectively are connected in series across a 12 volt battery supply. Calculate: a) the total resistance, b) the circuit current, c) the current through each resistor, d) the voltage drop across each resistor, e) verify that Kirchhoff’s voltage law, KVL holds true. MCQ MCQ MCQ In this simple parallel resistor example there are two distinct junctions for current. Junction one occurs at node B, and junction two occurs at node E. Thus we can use Kirchhoff’s Junction Rule for the electrical currents at both of these two Find distinct junctions, for I1 and those I2 entering the junction and for those currents flowing currents leaving the junction. In this simple parallel resistor example there are two distinct junctions for current. Junction one occurs at node B, and junction two occurs at node E. Thus we can use Kirchhoff’s Junction Rule for the electrical currents at both of these two distinct junctions, for those currents entering the junction and for those currents flowing leaving the junction.