GATE EE 2018 Set 1 — Question 65
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Electric Circuits → Transient & AC Steady-State → Series & Parallel Resonance
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Question
The voltage across the terminals and as shown in the figure, is a sinusoidal voltage having a frequency radian/s. When the inductor current is in phase with the voltage , the magnitude of the impedance (in ) seen between the terminals and is ________ (up to 2 decimal places).
Correct answer
50 to 50
Solution
The impedance seen between terminals and is given by the series combination of the inductor and the parallel combination of the resistor and capacitor :To simplify, multiply the numerator and denominator of the second term by the complex conjugate :It is given that the current is in phase with the voltage , which means the impedance must be purely resistive. Therefore, the imaginary part of must be zero:When this condition is met, the magnitude of the impedance is equal to its real part:Given values:
First, calculate :Now, calculate the magnitude of the impedance:Thus, the magnitude of the impedance is 50.00 .
First, calculate :Now, calculate the magnitude of the impedance:Thus, the magnitude of the impedance is 50.00 .
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