GATE 2025 EC – Question 61
The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by $V_I=10\sin100\pi t$, where time $t$ is in seconds.
The time duration (in ms, rounded off to two decimal places) for which the diode is forward biased during one period of the input is ____________.
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Correct answer: 13.26 to 13.40
Explanation
In the figure the battery has its positive (long) plate at the bottom, so it adds 5 V in series with $V_I$ around the loop. The diode conducts when $V_I+5>0$, i.e. $10\sin\theta>-5$, $\sin\theta>-0.5$. That holds for $\theta\in(-30^\circ,210^\circ)$, which is $240^\circ$ out of $360^\circ$, i.e. $2/3$ of the period. The period is $2\pi/100\pi=20$ ms, so the diode conducts for $\tfrac23\times20=13.33$ ms.