Q.Find the current $i$ in the circuit given below. Given, forward resistance of the diode is $r_f = 1\,\Omega$, $R = 2\,\Omega$ and $V = 10$ volts.

Diode Resistance: What Does It Even Mean?

Think of a diode as a one-way valve for electricity. When you push current through it in the forward direction, the diode doesn't just let everything through freely — it resists the flow, just like any other component. But here's the twist: that resistance isn't a fixed number like a resistor's 100 Ω. It changes depending on how much voltage you apply.

Why? Because a diode is a semiconductor device. Its current-voltage relationship follows the Shockley equation:

where $I_S$ is the reverse saturation current, $V$ is the applied voltage, $\eta$ is the ideality factor (usually 1 for silicon), and $V_T \approx 26 \text{ mV}$ at room temperature.

This exponential curve means that a tiny change in voltage can cause a huge change in current. So the "resistance" you measure depends entirely on where you are on that curve.

Two Kinds of Diode Resistance

Because the I-V curve is nonlinear, we define two different resistances — each useful in different situations.

1. Static (DC) Resistance

This is the simplest idea: just apply Ohm's law using the total voltage and total current at a given operating point.

For example, if a diode has 0.7 V across it and 10 mA flowing through it, its DC resistance is:

2. Dynamic (AC) Resistance

This is the more important one for circuit design. It tells you how the diode responds to small changes in voltage around a fixed operating point.

Mathematically, dynamic resistance is the slope of the I-V curve at that point:

For a forward-biased diode obeying the Shockley equation, we can derive a clean formula. Starting from:

(ignoring the -1, which is negligible in forward bias)

Differentiate:

Therefore:

At room temperature with $\eta = 1$ and $V_T = 26 \text{ mV}$:

So if the diode current is 10 mA, $r_d = 2.6 \ \Omega$ — much smaller than the 70 Ω DC resistance.

When Do You Use Each?

A Quick Example to Tie It Together

A silicon diode ($\eta = 1$) is forward biased with $V = 0.7 \text{ V}$ and carries $I = 20 \text{ mA}$.

Static resistance: …