This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Circuit Elements in the S-Domain”.
1. The resistance element __________ while going from the time domain to frequency domain.
a) does not change
d) increases exponentially
Explanation: The s-domain equivalent circuit of a resistor is simply resistance of R ohms that carries a current I ampere seconds and has a terminal voltage V volts-seconds. The resistance element does not change while going from the time domain to the frequency domain.
2. The relation between current and voltage in case of inductor is?
Explanation: Consider an inductor with an initial current Io. The time domain relation between current and voltage is v=Ldi/dt.
3. The s-domain equivalent of the inductor reduces to an inductor with impedance?
Explanation: If the initial energy stored in the inductor is zero, the equivalent circuit of the inductor reduces to an inductor with impedance sL ohms.
4. The voltage and current in a capacitor are related as?
Explanation: Consider an initially charged capacitor and the initial voltage on the capacitor is Vo. The voltage current relation in the time domain is i=Cdv/dt.
5. The s-domain equivalent of the capacitor reduces to an capacitor with impedance?
Explanation: The s-domain equivalent of the capacitor can be derived for the charged capacitor and it reduces to an capacitor with impedance 1/sC.
Explanation: Applying Kirchhoff’s law around the loop, we have V/s=1/sC I+RI. Solving above equation yields I=CV/(RCS+1)=(V/R)/(s+1/RC).
7. After taking the inverse transform of current in the circuit shown in question 6, the value of current is?
Explanation: We had assumed the capacitor is initially charged to Vo volts. By taking the inverse transform of the current, we get i=(V/R) e-t/RC.
8. The voltage across the resistor in the circuit shown in question 6 is?
Explanation: We can determine the voltage v by simply applying the ohm’s law from the circuit. And applying the Ohm’s law from the circuit v = Ri = Ve-t/RC.
Explanation: The given circuit is converted to parallel equivalent circuit. By taking the node equation, we get v/R+sCv=CV. Solving the above equation, v=V/(s+1/RC).
10. Taking the inverse transform of the voltage across the resistor in the circuit shown in question 9.
Explanation: By taking the inverse transform, we get v=Ve-t/RC=Ve-t/τ, where τis the time constant and τ = RC. And v is the voltage across the resistor.
Sanfoundry Global Education & Learning Series – Network Theory.
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