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

Concept:

• The depletion layer width depends upon the biasing of the diode.

• Forward bias decreases the depletion width.

• Reverse bias increases the depletion width.

• Greater reverse voltage produces a larger depletion region.

Step 1: Recall the effect of biasing on depletion width
For a p-n junction, \[ W \propto \sqrt{V_b+V_R} \] where \(V_R\) is the reverse bias voltage. Thus,

• Forward bias \(\rightarrow\) smaller depletion layer.

• Reverse bias \(\rightarrow\) larger depletion layer.

Step 2: Analyze diode \(D_1\)
From the circuit, diode \(D_1\) is forward biased. Hence its depletion width is the smallest among the three. \[ W_1=\text{minimum} \]

Step 3: Analyze diode \(D_2\)
Diode \(D_2\) is reverse biased. Therefore its depletion region is larger than that of \(D_1\). \[ W_2\gt W_1 \]

Step 4: Analyze diode \(D_3\)
Diode \(D_3\) is subjected to the maximum reverse bias. Hence its depletion layer becomes the largest. \[ W_3\gt W_2 \]

Step 5: Compare all depletion widths
Combining the above results, \[ W_3\gt W_2\gt W_1 \] Therefore, \[ \boxed{W_3\gt W_2\gt W_1} \] Hence, \[ \boxed{\text{Option (D)}} \]