GATE EE 2015 Set 1 — Question 55
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Electric Circuits → AC Power & Three-Phase → RMS & Average Values
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Question
The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in Volt) is given by . If the circuit is in steady state, then the rms value of the current (in Ampere) flowing in the circuit is ______.
Correct answer
9.9 to 10.1
Solution
The circuit contains two sources: an AC source and a DC source . By the superposition principle:
1.DC Analysis: Under steady state, the inductor acts as a short circuit. The DC current is:
2.AC Analysis: The AC source is , so and . The RMS value of the AC voltage is . The impedance is . The magnitude of the impedance is . The RMS value of the AC current is:
3.Total RMS Current: The total RMS current is the square root of the sum of the squares of the individual RMS components:
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