Semiconductors: Step-by-Step Worked Examples (6)

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Question

A silicon p-n junction diode has a knee voltage of 0.7 V. It is connected in series with a 1kΩ1\,k\Omega resistor and a 5 V battery in forward bias. Find: (a) current through the diode, (b) voltage across the resistor, (c) power dissipated in the diode, (d) what changes if we reverse the battery.

Solution — Step by Step

In forward bias, the diode acts like a fixed voltage drop of VD=0.7V_D = 0.7 V (knee voltage). Applying KVL around the loop:

Vbattery=VD+IRV_{\text{battery}} = V_D + I R

5=0.7+I10005 = 0.7 + I \cdot 1000

I=4.31000=4.3 mAI = \frac{4.3}{1000} = 4.3 \text{ mA}

Voltage across resistor: VR=IR=4.3×1031000=4.3V_R = IR = 4.3 \times 10^{-3} \cdot 1000 = 4.3 V.

Power dissipated in diode: PD=VDI=0.74.3×103=3.01 mWP_D = V_D \cdot I = 0.7 \cdot 4.3 \times 10^{-3} = 3.01 \text{ mW}.

In reverse bias, the diode allows only a tiny reverse saturation current (typically \simnA for silicon). For practical purposes, I0I \approx 0 in reverse bias. So VR0V_R \approx 0 and the entire 5 V appears across the diode.

(a) I=4.3I = 4.3 mA, (b) VR=4.3V_R = 4.3 V, (c) PD=3.01P_D = 3.01 mW, (d) reverse: I0I \approx 0, VD5V_D \approx 5 V.

Why This Works

The ideal-diode-with-knee-voltage model treats a forward-biased diode as a constant 0.7 V drop (silicon) or 0.3 V (germanium). This linearizes the exponential I-V characteristic into a piecewise straight line — accurate enough for circuit analysis at the JEE/NEET level.

In reverse bias, the diode behaves like an open circuit (until breakdown). This asymmetric conduction is what makes the diode useful as a rectifier.

For half-wave rectifier output, Vdc=Vm/πV_{dc} = V_m/\pi and Vrms=Vm/2V_{rms} = V_m/2. For full-wave: Vdc=2Vm/πV_{dc} = 2V_m/\pi and Vrms=Vm/2V_{rms} = V_m/\sqrt{2}. These formulas are tested directly almost every NEET year.

Alternative Method

Using the ideal diode (zero knee voltage): I=V/R=5/1000=5I = V/R = 5/1000 = 5 mA. This overestimates by 0.7 mA. For JEE questions, always check whether “ideal” or “silicon (0.7 V)” is specified.

Common Mistake

Students write I=V/R=5 mAI = V/R = 5\text{ mA}, ignoring the 0.7 V knee. Or worse, they subtract 0.7 V twice (once thinking it’s a battery, once as a drop). The diode is one element — one drop, applied once, in the direction of current flow.

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