Unit 5 - Direct Current (DC) PDF

Unit 5 Direct current(DC) Direct current (DC) is an electric current that is uni-directional, so the flow of charge is always in the same direction, figure (5.1). As opposed to alternating current, the direction and amperage of direct currents do not change. It is used in many household electronics...

Unit 5 Direct current(DC) Direct current (DC) is an electric current that is uni-directional, so the flow of charge is always in the same direction, figure (5.1). As opposed to alternating current, the direction and amperage of direct currents do not change. It is used in many household electronics and in all devices that use batteries. Fig. (5.1) direct current flow in electrical circuit and waveform Electromotive force in dc circuit EMF Electromotive force (EMF) is equal to the terminal potential difference when no current flows. EMF and terminal potential difference (V) are both measured in volts; however, they are not the same thing. EMF (ϵ) is the amount of energy (E) provided by the battery to each coulomb of charge (Q) passing through. The EMF can be written in terms of the internal resistance of the battery (r) where: ϵ = I(R+r) Which from Ohm’s law, we can then rearrange this in terms of the terminal resistance: ϵ = V+Ir The EMF of the cell can be determined by measuring the voltage across the cell using a voltmeter and the current in the circuit using an ammeter for various resistances. 03 Kirchhoff's rules Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low- frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies. Kirchhoff's current law Kirchhoff’s Current Law (KCL) states that for a parallel path (the total current entering a circuit's junction is exactly equal to the total current leaving the same junction), figure (5.2). Σ IIN = Σ IOUT. Fig. (5.2) Kirchhoff's current law Kirchhoff's voltage law Kirchhoff’s Voltage Law (KVL) is the second of his fundamental laws which states that for a closed loop the algebraic sum of all the voltages around any closed loop in a circuit is equal to zero, figure (5.3). ΣV = 0. 03  Fig. (5.4) Power dissipation in a direct current circuit If a current I flows through a given element in the circuit, losing voltage V in the process, then the power dissipated by that circuit element is the product of that current and voltage, figure (5.5): Power Rule: P = I × V Power is the amount of energy that is expended over a certain amount of time. In electronics, power dissipation is usually a measure of how much heat is being released due to inefficiencies in the circuitry. If you know the voltage drop across a component and the current through it, you can figure out the power dissipation using elementary math. hope is not lost. Using Ohm’s Law, we know Calculate voltage by multiplying the current and resistance and Calculate current through the division of voltage over resistance So we can change that power equation to: 00 The instantaneous rate at which this work is done is called the electric power, and is measured in watts (W). Expressed as an equation, the relationship between power, work, and time is where P is power in watts W is work in joules t is time in seconds Fig. (5.5) Power dissipated in the direct current circuit Heating Effect of Electric Current When an electric current passes through a conductor (like a high resistance wire) the conductor becomes hot after some time and produces heat. This is called heating effect of Electric Current, figure (5.6). Example 1. A bulb becomes hot after its use for some time. 03  o Instantaneous value: It is the value of voltage or current at any given time denoted by i or e. o Frequency: It is defined as the number of cycles per second made by an alternating quantity. The cycles are measured in hertz (Hz) or Cycle per second (c/s). o Time Taken: The time taken in seconds by a voltage or a current to complete one cycle is called time period. It is denoted by (T). o Waveform: It is a shape created by charting the instantaneous values of an alternating variable like voltage and current along the y-axis and the time (t) or angle (θ=ωt) along the x-axis. Effective Value of an alternating Current Values of AC voltage and current in a circuit may be given as peak value, average value, or rms value. Fig. (5.8) the effective value of AC current The effective value is also known as the RMS value or root mean square, which refers to the mathematical process by which the value is derived. The effective value is less than the maximum value, being equal to.707 times the maximum value, figure (5.8). Effective value (RMS) = peak value x 0.707 Example 5.2: The peak value of voltage in an AC circuit is 200 V. What is the RMS value of the voltage? E = 0.707Emax 03 E = 0.707 x 200 = 141.4 V Ohm's Law for AC circuit The AC analog to Ohm's law is where Z is the impedance of the circuit and V and I are the rms or effective values of the voltage and current, figure (5.9). Associated with the impedance Z is a phase angle, so that even though Z is also the ratio of the voltage and current peaks, the peaks of voltage and current do not occur at the same time. The phase angle is necessary to characterize the circuit and allow the calculation of the average power used by the circuit. Fig. (5.9) Ohm's Law for AC circuit Resistor-capacitor (RC) AC Circuit A circuit with a resistor, a capacitor, and an ac generator is called an RC circuit. A capacitor is basically a set of conducting plates separated by an insulator; thus, a steady current cannot pass through the capacitor. A simple circuit for charging a capacitor is shown in figure (5.10). The capacitive time constant is Where the capacitive time constant, denoted by the Greek letter (tau) 03  Fig. (5.10) (RC) AC Circuit Impedance (Z) of a series R-C circuit may be calculated, given the resistance (R) and the capacitive reactance (XC), figure (5.11). Where Fig. (5.11) Series: R-C circuit Impedance phasor diagram. Example 5.3: A 50 Ω XC and a 60 Ω resistance are in series across a 110V source. Calculate the impedance. 03 Z = √ (602 + 502) Z = √6100 = 78.1 Ω Resistor-Inductor (RL) AC Circuit A circuit with a resistor, an inductor, and an ac generator is an RL circuit, figure (5.12). When the switch is closed in an RL circuit, a back emf is induced in the inductor coil. The current, therefore, takes time to reach its maximum value, and the time constant, called the inductive time constant, is given by Fig. (5.12) (RL) AC Circuit Impedance (Z) of a series R-L circuit may be calculated, given the resistance (R) and the inductive reactance (XL), figure (5.13). Where 03  Fig. (5.13) Series: R-L circuit Impedance phasor diagram. Example 5.4 A coil which has an inductance of 40mH and a resistance of 2Ω is connected together to form a LR series circuit. If they are connected to a 20V DC supply. a). What will be the final steady state value of the current. b) What will be the time constant of the RL series circuit. 33 Resistor-Inductor-Capacitor (RLC) AC circuit Fig. (5.14) (RLC) AC Circuit Consider a circuit containing a resistor of resistance R, a inductor of inductance L and a capacitor of capacitance C connected across an alternating voltage source, figure (5.14). The applied alternating voltage is given by the equation. The phasor diagram is drawn with current as the reference phasor. The current is represented by the phasor as shown in figure (5.15). Fig. (5.15) phasor diagram for RLC Circuit Z is called impedance of the circuit. Uses of AC Circuit AC is the form of current that is mostly used in different appliances. Some of the examples of alternating current include audio signal, radio signal, etc. An alternating current has a wide advantage over DC as AC is able to transmit power over large distances without great loss of energy. 33 AC is used mostly in homes and offices mainly because the generating and transporting of AC across long distances is a lot easier. Meanwhile, AC can be converted to and from high voltages easily using transformers. AC is also capable of powering electric motors that further convert electrical energy into mechanical energy. Due to this, AC also finds its use in many large appliances like refrigerators, dishwashers and many other appliances. 33