Question

Three identical p-n junction diodes \(D_1\), \(D_2\) and \(D_3\) are connected across a battery as shown in the figure. If the widths of the depletion regions of \(D_1\), \(D_2\) and \(D_3\) are \(W_1\), \(W_2\) and \(W_3\), respectively, then the correct option is:

• A. \(W_2 \gt W_1 = W_3\)
• B. \(W_1 \gt W_2 \gt W_3\)
• C. \(W_3 = W_1 \gt W_2\)
• D. \(W_3 \gt W_2 \gt W_1\)

Hint:

Forward bias narrows the depletion layer while reverse bias widens it. More reverse voltage means a larger depletion width.

Answer 1

The Correct Option is D

Step 1: Recall what sets the depletion width.
The depletion region of a p-n junction grows or shrinks with the applied voltage. The relation is $W \propto \sqrt{V_b + V_R}$, where $V_R$ is the reverse-bias voltage.
Step 2: Effect of forward bias.
Forward bias pushes majority carriers toward the junction, so it narrows the depletion layer. A forward-biased diode has the smallest width.
Step 3: Effect of reverse bias.
Reverse bias widens the depletion layer, and a larger reverse voltage widens it more.
Step 4: Diode D1.
From the circuit, $D_1$ is forward biased, so $W_1$ is the smallest of the three.
Step 5: Diode D2.
$D_2$ is reverse biased, so $W_2 > W_1$.
Step 6: Diode D3 and the conclusion.
$D_3$ carries the largest reverse bias, so $W_3$ is the widest: $W_3 > W_2 > W_1$, which is option D.
\[ \boxed{W_3 > W_2 > W_1} \]