GATE EC 2022 Set 1 — Question 39
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Network Theory → Transient & AC Analysis → Sinusoidal Steady-State
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Question
Consider the circuit shown in the figure with input in volts. The sinusoidal steady state current flowing through the circuit is shown graphically (where is in seconds). The circuit element can be ________.
Correct answer
(B) an inductor of 1 H
Solution
The input voltage is , which implies . The phasor voltage is .From the current graph:
.From the circuit diagram, . Therefore:
.Since and , we have:
.Thus, the element is an inductor of .
- The peak current is .
- The current waveform is zero at and increasing. For a sine wave , the zero crossing is at . Since this waveform crosses zero at , it is shifted to the right, meaning it lags the voltage by radians ().
- Thus, .
.From the circuit diagram, . Therefore:
.Since and , we have:
.Thus, the element is an inductor of .
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