GATE 2026 EE – Question 61
Consider the circuit shown. Assume that the diode ($D$) is ideal.
Given $v_s=100\sin(2\pi50t)$ V, $V_{dc}=50$ V, and $R=10\ \Omega$, the average value of the current through the diode is ___________ A.
(Round off to two decimal places)
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 1.08 to 1.10
Explanation
The diode conducts when $v_s>V_{dc}=50$ V, i.e. $100\sin\theta>50$, for $\theta$ from $\pi/6$ to $5\pi/6$. There $i=\dfrac{100\sin\theta-50}{10}$. The average over the period is $I_{avg}=\dfrac1{2\pi}\int_{\pi/6}^{5\pi/6}\dfrac{100\sin\theta-50}{10}d\theta=\dfrac1{20\pi}\left[100(\cos\tfrac\pi6-\cos\tfrac{5\pi}6)-50\cdot\tfrac{2\pi}{3}\right]=\dfrac{173.2-104.7}{62.83}=1.09$ A.