Electrical Circuit & Network

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1 Electrical Circuit & Network January Website: Electrical Engg.(MCQ) Question and Answer for the students of SSC(JE), PSC(JE), BSNL(JE), WBSEDCL, WBSETCL, WBPDCL, CPWD and State and Central Service Examination 2nd Year 3rd Semester

2 Unit-1 (Basic concept of Electrical Circuit) Electrical Circuit & Network Contents i. Energy source ii. AC wave form and definition: Cycle, Time period, Frequency, Average value, R.M.S. value (root mean square), Form factor, Peak factor, Phase, Phase difference iii. A.C through pure resistive circuit iv. A.C. through pure inductive circuit v. A.C. through pure capacitive circuit Unit-2 (Single phase AC circuits & Resonance) i. Study of j-operator ii. A.C. through R-L series circuit, R-C series circuit, R-L-C series circuit iii. Impedance, Reactance, Inductive reactance, Capacitance reactance, Power factor, Type of power factor, Power triangle, Impedance table, Power triangle table, Active power Reactive power, Apparent power: Parallel AC circuit i. Impedance method ii. Admittance method: Series resonance circuit i. Definition, resonance frequency, Properties of series resonance ii. iii. iv. Half power bandwidth Q Factor Why Q- Factor is called voltage magnification factor v. Selectivity vi. vii. Acceptor Circuit Voltage resonance Parallel Resonance circuit i. Definition ii. Resonance frequency, Current at resonance iii. Properties of parallel resonance iv. Q-Factor v. Rejector circuit Unit-3(Principles of circuit Analysis)

3 i. Mesh analysis ii. Nodal analysis Unit-4(Network Theorems) i. Source conversion (voltage source to current source, Current source to voltage source) ii. Thevenin s Theorem, Area of application, Limitation of Thevenini s Theorem iii. Norton s Theorem, Area of application, Limitation of Norton s Theorem iv. Maximum Power Transfer Theorem, Application, Limitation v. Superposition Theorem Unit-5(Transient Analysis) i. Introduction ii. iii. Transient response in R-L dc circuit, Voltage drop across resistor, Voltage drop across inductor, Total voltage drops Transient response in R-C circuit, Voltage drop across resistor, Voltage drop across capacitor Unit-6(Laplace Transform) i. Introduction, Definition ii. iii. iv. Properties of Laplace Transform Laplace transform of unit step function Laplace transform of exponential function v. Laplace transform of Ramp function vi. vii. viii. ix. Obtain the Laplace transform of a function Obtain the Laplace transform of a function Obtain the Laplace transform of a function Obtain the Laplace transform of a parabolic function x. Obtain the Laplace transform of a function of f(t)= e -at sinwt xi. xii. xiii. xiv. xv. Obtain the Laplace transform of a function of f(t) = e -at coswt Proof the initial value theorem in context of Laplace Transform Proof the final value theorem in context of Laplace Transform Obtain the Laplace transform of unit impulse function Laplace transform of a derivatives Electrical Circuit & Network Unit-1 (Basic concept of Electrical Circuit)

4 Circuit elements Voltage Current Power Energy source R(Ω) V=IR i= V R P= I 2 R I 2 Rt L(H) V = L di dt i= 1 t vdt L 0 P= Li di dt 1 2 LI2 C(F) V= 1 t idt i=c dv C 0 dt P=CV dv dt 1 2 CV2 Energy source: There are basic two types of energy source for driving the electrical circuit. 1. Independent energy source (ac or dc) (a) Voltage source (b) Current source 2. Dependent energy source (ac or dc) (a) Voltage dependent voltage source (b) Current dependent voltage source (c) Voltage dependent current source (d) Current dependent current source Voltage source: The source which can deliver power to load in such a way that the voltage across its terminal remains constant irrespective of the current drawn from the supply. Example: generator and battery. Current source: The source which can deliver power to load in such a way that current delivered by it remain constant irrespective of the voltage. Example: most of the semiconductor devices like diode and transistor. Ideal voltage source: The Ideal voltage source is one which has zero internal impedance. Ideal current source: The Ideal current source is one which has infinite internal impedance. Cycle: One complete set of positive and negative value of an alternating quantity is known as cycle. One complete set is said to be or 2 rad.

5 Time period: The time taken in second to complete one cycle of an alternating quantity is known as time period. It is denoted by T. Frequency: The number of cycle that can occur in one second is called the frequency. It is denoted by f. f = 1 T Average value: In general, the average value of a periodic function x(t) can be represented as t Xav = x(t)dt 0 In case of a sinusoidal wave, the average value will be represented as (say for voltage) Vav = 1 t V m sinωtd(ωt) 0 = V m cosωt 0 = V m [ - cos+ cos0] = V m [1 + 1] = 2V m Similarly, Iav = 2I m Note: It may be noted that average value of the sinusoidal wave is computed for half cycle as the average of the sine wave would be zero for a complete cycle. R.M.S. value (root mean square): The R.M.S. value of an alternating current is given by the steady (d.c.) current when flowing through a given circuit for a given time produces the same heat as produces by the alternating current when flowing through the same circuit for the same time. If the sinusoidal wave form of current and voltage is given I = Imsinωt V = Vmsinωt Then, R.M.S. value will be Ir.m.s. = I m 2 and Vr.m.s. = V m 2 Form factor: It is the ratio of R.M.S. value to average value.

6 R.M.S. value Form factor = Average value Peak factor: It is the ratio of maximum value to R.M.S. value = Im 2 2Im = 1.11 (fixed) Max value Peak factor = R.M.S.value = V m Vm 2 = (fixed) Phase: The phase of an alternating quantity is the fraction of the time period or cycle over which the alternating quantity has passed from the reference point. Phase difference: When two or more alternating quantity have the same frequency but different maximum or zero point, they are known to have the phase difference. Here, θ is the phase difference between V1 and V2. A.C through pure resistive circuit:

7 VR = IR In case of pure resistive circuit the voltage and current are in same phase. There is no phase difference between them. And Power factor is unity (Since cos0 0 = 1). A.C. through pure inductive circuit: VL = IXL and XL = 2fL In case of pure inductive circuit current lags the voltage by And power factor is zero (Since cos90 0 = 0). A.C. through pure capacitive circuit:

8 1 VC = IXC and XC = 2fC In case of pure capacitive circuit the current leads the voltage by 90 0 and the power factor is zero (Since cos90 0 = 0) Circuit connection Phasor diagram Wave form Phase angle Power factor Resistive No phase difference between V and I unity Inductive Current lags the voltage by 90 0 zero Capacitive Current leads the voltage by 90 0 zero

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