GATE EC 2015 Set 2 — Question 16
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Network Theory → Transient & AC Analysis → Sinusoidal Steady-State
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Question
The voltage () across the capacitor (in Volts) in the network shown is ______.
Correct answer
100 to 100
Solution
In a series RLC circuit, the source voltage is related to the voltages across the resistor (), inductor (), and capacitor () by the phasor relationship:Given:
Substituting the values:Taking the square root on both sides:Case 1: (Magnitude cannot be negative)
Case 2: Thus, the voltage across the capacitor is .
Substituting the values:Taking the square root on both sides:Case 1: (Magnitude cannot be negative)
Case 2: Thus, the voltage across the capacitor is .
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