Question

When the forward bias voltage in a semiconductor diode is changed from 0·8 V to 1·0 V, the forward current changes by 2·0 mA. The forward bias resistance of the diode will be :

• A. 200 \(\Omega\)
• B. 175 \(\Omega\)
• C. 100 \(\Omega\)
• D. 125 \(\Omega\)

Hint:

Always convert milli-units (like \(\text{mA} = 10^{-3}\text{ A}\)) to standard SI units before applying Ohm's law variants, ensuring you don't end up with an incorrect factor of 10 in your final answer.

Answer 1

The Correct Option is C

Concept: A semiconductor p-n junction diode displays a non-linear voltage-current relationship. Because its $I$-$V$ characteristic curve is non-linear, its resistance is not constant. Instead, we calculate its dynamic resistance (also called AC or forward bias resistance, \(r_d\)). Dynamic resistance is defined as the ratio of a small change in voltage across the diode (\(\Delta V\)) to the resulting change in current through it (\(\Delta I\)): \[ r_d = \frac{\Delta V}{\Delta I} \]

Step 1: Computing the change in forward bias voltage (\(\Delta V\)).
The forward bias voltage is modified across two specific operating conditions:
• Initial voltage, \(V_1 = 0.8\text{ V}\)
• Final voltage, \(V_2 = 1.0\text{ V}\) The net change in voltage is: \[ \Delta V = V_2 - V_1 = 1.0\text{ V} - 0.8\text{ V} = 0.2\text{ V} \]

Step 2: Converting current to standard SI units and computing (\(\Delta I\)).
The question states that the change in forward current is: \[ \Delta I = 2.0\text{ mA} \] To perform accurate calculations, we convert milliamperes (mA) into the standard SI unit of Amperes (A): \[ \Delta I = 2.0 \times 10^{-3}\text{ A} = 0.002\text{ A} \]

Step 3: Calculating the forward dynamic resistance.
Using the dynamic resistance formula: \[ r_d = \frac{\Delta V}{\Delta I} \] Substitute the calculated values: \[ r_d = \frac{0.2\text{ V}}{2.0 \times 10^{-3}\text{ A}} \] To simplify, move the power of ten from the denominator to the numerator: \[ r_d = \frac{0.2}{2.0} \times 10^3 = 0.1 \times 1000 = 100\text{ }\Omega \] The forward bias resistance of the diode is \(100\text{ }\Omega\), matching Option (C).