# Network Theory Questions and Answers – The Concept of Complex Frequency

This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “The Concept of Complex Frequency”.

1. The solution of differential equations for networks is of the form?
a) i(t)=Kn e⁡(sn t)
b) i(t)=Kn e⁡(-sn t)
c) i(t)=-Kn e⁡(-sn t)
d) i(t)=-Kn e⁡(sn t)

Explanation: The solution of differential equations for networks is of the form
i(t)=Kn e⁡(sn t) where Sn is a complex number which is a root of the characteristic equation.

2. The real part of the complex frequency is called?
b) neper frequency
c) sampling frequency
d) angular frequency

Explanation: The complex number consists of two parts, the real part and the imaginary part. The real part of the complex frequency is called neper frequency.

3. The imaginary part of the complex frequency is called?
a) angular frequency
b) sampling frequency
c) neper frequency

Explanation: The complex number consists of two parts, the real part of the complex frequency is called radian frequency. The radian frequency is expressed in radian/sec and is related to the frequency or the periodic time.

4. The ratio of transform voltage to the transform current is defined as _________ of the resistor.
a) transform voltage
b) transform current
c) transform impedance

Explanation: Transform impedance of the resistor is defined as the ratio of transform voltage to the transform current and is expressed as ZR(s) = VR(s)/IR(s) = R.

5. The ratio of transform current to the transform voltage is defined as ________ of the resistor.
b) transform impedance
c) transform current
d) transform voltage

Explanation: Transform admittance of the resistor is defined as the ratio of transform current to the transform voltage and it is also defined as the reciprocal of transform impedance. YR(s) = IR(s)/VR(s) = G.

6. The transform impedance of the inductor is?
a) L
b) 1/L
c) sL
d) 1/sL

Explanation: Considering the sum of the transform voltage and the initial current voltage as V1(s) we have the transform impedance of the inductor. The transform impedance of the inductor is ZL(s) = V1(s)/IL(s) = sL.

7. The transform admittance of the inductor is?
a) 1/sL
b) sL
c) 1/L
d) L

Explanation: The transform admittance of the inductor is YL(s) = I1(s)/VL(s) = 1/sL where I1(s) is the total transform current through the inductor L.

8. The equivalent transform circuit contains an admittance of value ____ and equivalent transform current source.
a) 1/L
b) 1/sL
c) L
d) sL

Explanation: The time domain representation of inductor L has initial current iL(0+). The equivalent transform circuit contains an admittance of value 1/sL and equivalent transform current source.

9. The transform impedance of the capacitor is?
a) C
b) 1/C
c) sC
d) 1/sC

Explanation: The transform impedance of the capacitor is the ratio of the transform voltage V1(s) to the transform current IC(s) and is ZC(s) = 1/Cs.

10. The transform admittance of the capacitor is?
a) 1/sC
b) sC
c) 1/C
d) C

Explanation: The transform admittance of the capacitor is the ratio of transform current I1(s) to transform voltage VC(s) and is YC(s) = sC.

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