This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Impedence Diagram”.

1. Impedance is a complex quantity having the real part as _______ and the imaginary part as ______

a) resistance, resistance

b) resistance, reactance

c) reactance, resistance

d) reactance, reactance

View Answer

Explanation: Almost all electric circuits offer impedance to the flow of current. Impedance is a complex quantity having the real part as resistance and the imaginary part as reactance.

2. The voltage function v(t) in the circuit shown below is?

a) v(t) = V_{m} e^{-tjω}

b) v(t) = V_{m}e^{tjω}

c) v(t) = e^{tjω}

d) v(t) = e^{-tjω}

View Answer

Explanation: The voltage function v(t) in the circuit is a complex function and is given by v(t) = V

_{m}e

^{tjω}=Vm(cosωt+jsinωt).

3. The current i(t) in the circuit shown above is?

a) i(t)=(V_{m}/(R-jωL))e^{tjω}

b) i(t)=(V_{m}(R+jωL)) e^{tjω}

c) i(t)=(V_{m}(R-jωL)) e^{tjω}

d) i(t)=(V_{m}/(R+jωL)) e^{tjω}

View Answer

Explanation: i(t)=I

_{m}e

^{tjω}. V

_{m}e

^{tjω}=RI

_{m}e

^{tjω}+L d/dt (I

_{m}e

^{tjω}). V

_{m}e

^{tjω}=RI

_{m}e

^{tjω}+L I

_{m}(jω)e

^{tjω}. I

_{m}= V

_{m}/(R+jωL). i(t)=(V

_{m}/(R+jωL)) e

^{tjω}.

4. The impedance of the circuit shown below is?

a) R + jωL

b) R – jωL

c) R + 1/jωL

d) R – 1/jωL

View Answer

Explanation: Impedance is defined as he ratio of the voltage to current function. The impedance of the circuit Z= V

_{m}e

^{tjω}/((V

_{m}/(R+jωL)) e

^{tjω})=R+jωL.

5. The magnitude of the impedance of the circuit shown above.

a) √( R+ωL)

b) √(R-ωL)

c)√(R^{2}+(ωL)^{2} )

d) √(R^{2}-(ωL)^{2} )

View Answer

Explanation: Complex impedance is the total opposition offered by the circuit elements to ac current and can be displayed on the complex plane. The magnitude of the impedance of the circuit is √(R

^{2}+(ωL)

^{2}).

6. The phase angle between current and voltage in the circuit shown above is?

a) tan^{-1}ωL/R

b) tan^{-1}ωR/

c) tan^{-1}R/ωL

d) tan^{-1}L/ωR

View Answer

Explanation: The angle between impedance and reactance is the phase angle between the current and voltage applied to the circuit. θ=tan

^{-1}ωL/R

7. The voltage function v(t) in the circuit shown below is?

a) v(t) = e^{-tjω}

b) v(t) = e^{tjω}

c) v(t) = V_{m}e^{tjω}

d) v(t) = V_{m}e^{-tjω}

View Answer

Explanation: If we consider the RC series circuit and apply the complex function v(t) to the circuit then voltage function is given by v(t)= V

_{m}e

^{tjω}.

8. The impedance of the circuit shown above is?

a) R + jωC

b) R – jωC

c) R + 1/jωC

d) R – 1/jωC

View Answer

Explanation: The impedance of the circuit shown above is R + 1/jωC. Here the impedance Z consists resistance which is real part and capacitive reactance which is imaginary part of the impedance.

9. The magnitude of the impedance of the circuit shown above is?

a) √(R+1/ωC)

b) √(R-1/ωC)

c) √(R^{2}+(1/ωC)^{2} )

d) √(R^{2}-(1/ωC)^{2} )

View Answer

Explanation: The magnitude of the impedance of the circuit shown above is √(R

^{2}+(1/ωC)

^{2}). Here the impedance is the vector sum of the resistance and the capacitive reactance.

10. The angle between resistance and impedance in the circuit shown above.

a) tan^{-1}1/ωRC

b) tan^{-1}C/ωR

c) tan^{-1}R/ωC

d) tan^{-1}ωRC

View Answer

Explanation: The angle between resistance and impedance in the circuit shown above tan

^{-1}1/ωRC. The angle between resistance and impedance is the phase angle between the applied voltage and current in the circuit.

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