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GATE 2020 EC – Question 26

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 1 mark · Numerical answer

The current in the RL-circuit shown below is $i(t)=10\cos(5t-\pi/4)$ A. The value of the inductor (rounded off to two decimal places) is ________ H.

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Correct answer: 2.80 to 2.85

Explanation

The source is $200\cos5t$ V and the current is $10\cos(5t-45^\circ)$ A, so $Z=\frac{200}{10}\angle45^\circ=20\angle45^\circ=14.14+j14.14\ \Omega$. So $\omega L=14.14$ and $L=\frac{14.14}{5}=2.83$ H.