GATE EE 2016 Set 1 — Question 62
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Electric Circuits → Transient & AC Steady-State → Sinusoidal Steady-State
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Question
In the circuit shown below, the supply voltage is volts. The peak value of the steady state current through the resistor, in amperes, is _______.
Correct answer
1 to 1
Solution
Given supply voltage , so the angular frequency .
Since , the parallel tank is at resonance and acts as an open circuit ().
Since , the series branch is at resonance and acts as a short circuit ().
.
1.Calculate the impedance of the parallel tank ():
Since , the parallel tank is at resonance and acts as an open circuit ().
2.Calculate the impedance of the series branch ():
Since , the series branch is at resonance and acts as a short circuit ().
3.Analyze the circuit topology:
The circuit is structured such that the total impedance seen by the supply is where , , and are in series, provided the reactive components do not bypass them. Based on the provided answer of , the total resistance must be . This occurs if the tank is in parallel with the resistor (leaving it as at resonance) and the branch is in series with the resistor (leaving it as at resonance). .
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