## Electrical Circuit Theory Solved Objective Questions asked in GATE, IES:

[1] The period of the signal x(t) = 8 sin (0.8πt + π /4) is [GATE 2010]
A. 0.4πs
B. 0.8πs
C. 1.25s
D. 2.5s

[2] The switch in the circuit has been closed for a long time. It is opened at t=0. At t=0+,the current through the 1μF capacitor is [GATE 2010]
A. 0A
B. 1A
C. 1.25A
D. 5A

[3] The second harmonic component of the periodic waveform given in the figure has an amplitude of [GATE 2010]
A. 0
B. 1
C. 2/π
D. √5

[4] As shown in the figure, a 1 resistance is connected across a source that has a load line v+i=100. The current through the resistance is [GATE 2010]
A. 25A
B. 50A
C. 100A
D. 200A

[5] If the electrical circuit of figure (b) is an eqiuvalent of the coupled tank system of figure (a), then [GATE 2010]

A. A,B are resistances and C,D capacitances
B. A,C are resistances and B,D capacitances
C. A,B  are capacitances and C,D resistances
D. A,C are capacitances are and B,D resistances

[6] If the 12Ω resistor draws a current of 1A as shown in the figure, the value of resistance R is [GATE 2010]
A. 4Ω
B. 6Ω
C. 8Ω
D. 18Ω

[7] The two-port network P shown in the figure has ports 1 and 2, denoted by terminals (a,b) and (c,d), respectively. It has an impedence matrix Z with parameters denoted by Zij. A 1Ω resistor is connected in series with the network at port 1 as shown in the figure. The impedance matrix of the modified two-port network (shown as a dashed box) is [GATE 2010]

[8] The Maxwell's bridge shown in the figure is at balance.The parameters of the inductive coil are [GATE 2010]

A. R=R2R3/R4, L=C4R2R3
B. L=R2R3/R4, R=C4R2R3
C. R=R4/R2R3, L=1(C4R2R3)
D. L=R4/R2R3, R=1/(C4R2R3)

Statement for Q9 & Q10:
The L-C circuit shown in the figure has an inductance L=1mH and a capacitance C=10μF
Question [9]: The initial current through the inductor is zero, while the initial capacitor voltage is 100V. The switch is closed at t=0. The current i through the circuit is: [GATE 2010]
A. 5cos(5x103t)A
B. 5sin(104t)A
C. 10cos(5x103t)A
D. 10sin(104t)A

Question [10]: The L-C circuit of statement is used to commutate a thyristor, which is initially carrying a current of 5A as shown in the figure below. The values and initial conditions of L and C are the same as in statement. The switch is closed at  t=0. If the forward drop is negligible, the time taken for the device to turn off is [GATE 2010]

A. 52μs
B. 156μs
C. 312μs
D. 26μs

[11] The voltage applied to a circuit is 100√2 cos(100πt) volts and the circuit draws a current of  10√2sin(100πt +π/4) amperes. Taking the voltage as the reference phasor, the phasor representation of the current in amperes is [GATE 2011]
A. 10√2∠-  π/4
B. 10∠-  π/4
C. 10∠+ π/4
D. 10√2∠+ π/4

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