Question

An $AC$ source is given by $V=2\sin \left(t\right)\text{V}$. It is connected across a diode and a resistor of resistance $2\Omega$ as shown in the figure below. Find the current through the circuit at $t=\frac{\pi }{6}$ and $t=\frac{5\pi }{6}$ respectively. Assume zero resistance of diode in forward biasing and infinite resistance in reverse biasing.

• A. $0,0.5\text{A}$
• B. $0,0$
• C. $0.5\text{A},0$
• D. $0.5\text{A},0.5\text{A}$

Answer 1

The correct option is C $0.5\text{A},0$

The voltage source $\left(V\right)$ can be plotted with respect to time $\left(t\right)$ as


At $t=\frac{\pi }{6}$, $\text{V}$ is in positive half cycle, and therefore, the diode is forward biased.

$\Rightarrow R_{diode}=0$

$V=2\sin \left(\frac{\pi }{6}\right)=1\text{V}$

Using,

$i=\frac{V}{R}=\frac{1}{2}=0.5\text{A}$

At $t=\frac{5\pi }{6}$, $V$ is in negative half cycle and therefore, the diode is reverse biased.

$\Rightarrow R_{diode}=\infty$

Thus, the current is zero.

Hence, option $\left(B\right)$ is correct.