# Sinusoidal Response of an R-C Circuit MCQ’s

This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Sinusoidal Response of an R-C Circuit”.

1. The particular current obtained from the solution of i in the sinusoidal response of R-C circuit is?

a) i_{p} = V/√(R^{2}+(1/ωC)^{2}) cos(ωt+θ+tan^{-1}(1/ωRC))

b) i_{p} = -V/√(R^{2}+(1/ωC)^{2}) cos(ωt+θ-tan^{-1}(1/ωRC))

c) i_{p} = V/√(R^{2}+(1/ωC)^{2}) cos(ωt+θ-tan^{-1}(1/ωRC))

d) i_{p} = -V/√(R^{2}+(1/ωC)^{2}) cos(ωt+θ+tan^{-1}(1/ωRC))

2. The value of ‘c’ in complementary function of ‘i’ is?

a) c = V/R cosθ+V/√(R^{2}+(1/(ωC))^{2}) cos(θ+tan^{-1}(1/ωRC))

b) c = V/R cosθ+V/√(R^{2}+(1/(ωC))^{2}) cos(θ-tan^{-1}(1/ωRC))

c) c = V/R cosθ-V/√(R^{2}+(1/(ωC))^{2}) cos(θ-tan^{-1}(1/ωRC))

d) c = V/R cosθ-V/√(R^{2}+(1/(ωC))^{2}) cos(θ+tan^{-1}(1/ωRC))

3. In the sinusoidal response of R-C circuit, the complementary function of the solution of i is?

a) i_{c} = ce^{-t/RC}

b) i_{c} = ce^{t/RC}

c) i_{c} = ce^{-t/RC}

d) i_{c} = ce^{t/RC}

4. The complete solution of the current in the sinusoidal response of R-C circuit is?

a) i = e^{-t/RC}[V/R cosθ+V/√(R^{2}+(1/(ωC))^{2}) cos(θ+tan^{-1}(1/ωRC))+V/√(R^{2}+(1/ωC)^{2}) cos(ωt+θ+tan^{-1}(1/ωRC)]

b) i = e^{-t/RC}[V/R cosθ-V/√(R^{2}+(1/ωC)^{2}) cos(θ+tan^{-1}(1/ωRC))-V/√(R^{2}+(1/ωC)^{2}) cos(ωt+θ+tan^{-1}(1/ωRC)]

c) i = e^{-t/RC}[V/R cosθ+V/√(R^{2}+(1/ωC)^{2}) cos(θ+tan^{-1}(1/ωRC))-V/√(R^{2}+(1/ωC)^{2}) cos(ωt+θ+tan^{-1}(1/ωRC)]

d) i = e^{-t/RC}[V/R cosθ-V/√(R^{2}+(1/(ωC))^{2}) cos(θ+tan^{-1}(1/ωRC))+V/√(R^{2}+(1/ωC)^{2}) cos(ωt+θ+tan^{-1}(1/ωRC)]

5. In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 50cos (102t+π/4), resistance R = 10Ω and capacitance C = 1µF. The particular integral of the solution of ‘i_{p}’ is?

a) i_{p} = (4.99×10^{-3}) cos(100t+π/4-89.94^{o})

b) i_{p} = (4.99×10^{-3}) cos(100t-π/4-89.94^{o})

c) i_{p} = (4.99×10^{-3}) cos(100t-π/4+89.94^{o})

d) i_{p} = (4.99×10^{-3}) cos(100t+π/4+89.94^{o})

6. In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 50cos (102t+π/4), resistance R = 10Ω and capacitance C = 1µF. The complete solution of ‘i’ is?

a) i = c exp (-t/10^{-5}) – (4.99×10^{-3}) cos(100t+π/2+89.94^{o})

b) i = c exp (-t/10^{-5}) + (4.99×10^{-3}) cos(100t+π/2+89.94^{o})

c) i = -c exp(-t/10^{-5}) + (4.99×10^{-3}) cos(100t+π/2+89.94^{o})

d) i = -c exp(-t/10^{-5}) – (4.99×10^{-3}) cos(100t+π/2+89.94^{o})

7. In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 50cos (102t+π/4), resistance R = 10Ω and capacitance C = 1µF. The complementary function of the solution of ‘i’ is?

a) i_{c} = c exp (-t/10^{-10})

b) i_{c} = c exp(-t/10^{10})

c) i_{c} = c exp (-t/10^{-5})

d) i_{c} = c exp (-t/10^{5})

8. In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 50cos (102t+π/4), resistance R = 10Ω and capacitance C = 1µF. The current flowing in the circuit at t = 0 is?

a) 1.53

b) 2.53

c) 3.53

d) 4.53

9. In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 50cos (102t+π/4), resistance R = 10Ω and capacitance C = 1µF. The value of c in the complementary function of ‘i’ is?

a) c = (3.53-4.99×10^{-3}) cos(π/4+89.94^{o})

b) c = (3.53+4.99×10^{-3}) cos(π/4+89.94^{o})

c) c = (3.53+4.99×10^{-3}) cos(π/4-89.94^{o})

d) c = (3.53-4.99×10^{-3}) cos(π/4-89.94^{o})

10. In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 50cos (102t+π/4), resistance R = 10Ω and capacitance C = 1µF. The complete solution of ‘i’ is?

a) i = [(3.53-4.99×10^{-3})cos(π/4+89.94^{o})] exp(-t/0.00001)+4.99×10^{-3}) cos(100t+π/2+89.94^{o})

b) i = [(3.53+4.99×10^{-3})cos(π/4+89.94^{o})] exp(-t/0.00001)+4.99×10^{-3}) cos(100t+π/2+89.94^{o})

c) i = [(3.53+4.99×10^{-3})cos(π/4+89.94^{o})] exp(-t/0.00001)-4.99×10^{-3}) cos(100t+π/2+89.94^{o})

d) i = [(3.53-4.99×10^{-3})cos(π/4+89.94^{o})] exp(-t/0.00001)-4.99×10^{-3}) cos(100t+π/2+89.94^{o})

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