Q.Dynamic resistance of a diode is given by ___.
🔒You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.
🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Diode Resistance Calculation
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:
I=IS(eV/ηVT−1)
where IS is the reverse saturation current, V is the applied voltage, η is the ideality factor (usually 1 for silicon), and VT≈26 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.
RDC=IV
For example, if a diode has 0.7 V across it and 10 mA flowing through it, its DC resistance is:
RDC=0.010.7=70 Ω
Static resistance tells you the average opposition to current at that specific point. It's useful for power calculations (P=I2RDC) but not for small signal analysis.
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:
rd=dIdV
For a forward-biased diode obeying the Shockley equation, we can derive a clean formula. Starting from:
I=ISeV/ηVT
(ignoring the -1, which is negligible in forward bias)
Differentiate:
dVdI=ηVTI
Therefore:
rd=dIdV=IηVT
rd=IηVT
At room temperature with η=1 and VT=26 mV:
rd=I26 mV
So if the diode current is 10 mA, rd=2.6 Ω — much smaller than the 70 Ω DC resistance.
Dynamic resistance is not a physical resistor inside the diode. It's a small-signal model parameter. You cannot use it with DC voltages or large signals — only for tiny variations around the operating point.
When Do You Use Each?
| Situation | Use |
|---|---|
| Finding DC power dissipation | RDC |
| Designing a biasing circuit | RDC |
| Analyzing small-signal amplifier response | rd |
| Calculating voltage regulation in a Zener diode | rd (called Zener impedance) |
A Quick Example to Tie It Together
A silicon diode (η=1) is forward biased with V=0.7 V and carries I=20 mA.
Static resistance: …
Why this formula?
Diode Resistance: Why It Changes with Operating Point
A diode is not a linear resistor. Its current-voltage relationship follows the Shockley equation:
I=IS(eV/ηVT−1)
where IS is the reverse saturation current, η is the ideality factor (typically 1–2), and VT=kT/q≈26mV at room temperature.
Because the I–V curve is exponential, the diode's resistance depends entirely on where you are on that curve. There are two distinct resistances we care about: DC resistance (static) and AC resistance (dynamic).
DC Resistance (Static Resistance)
Definition: The ratio of the DC voltage across the diode to the DC current through it at a given operating point.
RDC=IV
Why this formula? It's simply Ohm's law applied to the DC values. If you put 0.7 V across a diode and get 10 mA through it, the DC resistance is 0.7/0.01=70Ω. But this number is misleading — it doesn't tell you how the diode responds to a small change in voltage.
DC resistance is rarely useful in circuit analysis because diodes are never operated as fixed resistors. It's just a snapshot at one point.
AC Resistance (Dynamic Resistance)
Definition: The slope of the I–V curve at a given operating point — i.e., the ratio of a small change in voltage to the resulting small change in current.
rd=dIdV
Why this formula? For small signals (like an AC voltage superimposed on a DC bias), the diode behaves approximately linearly around that bias point. The dynamic resistance is the local slope of the I–V curve.
Now let's derive the actual expression.
Derivation of rd=IηVT
Start from the Shockley equation. For forward bias where V≫VT, the −1 term is negligible:
I≈ISeV/ηVT
Take the derivative with respect to V:
dVdI=IS⋅ηVT1⋅eV/ηVT=ηVTI
The dynamic resistance is the reciprocal:
rd=dIdV=IηVT
rd=IηVT
Key insight: The dynamic resistance is inversely proportional to the DC current I. At higher currents, the diode's I–V curve is steeper, so a small voltage change produces a larger current change — meaning lower resistance.
Why This Matters …
Because a diode's I-V curve is non-linear, its dynamic (AC) resistance is defined locally as the ratio of a small voltage change to the resulting small current change, rather than as a fixed constant. …
Dynamic (AC) resistance of a diode is defined as the ratio of a small change in voltage to the resulting small change in current, at a given operating point on its (non-linear) V-I curve.
Unlike a fixed ohmic resistor, a diode's I-V curve is non-linear, so its resistance varies with operating point. The dynamic resistance is defined as:
…
- CBSE 2026Set 55/3/11 markMCQQ.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 Ω (B) 175 Ω (C) 100 Ω (D) 125 Ω
›Reveal solutionSolution
The forward bias resistance (dynamic resistance) is the ratio of change in voltage to change in current. Here, ΔV=0.2 V and ΔI=2.0 mA, so rd=0.2/(2.0×10−3)=100 Ω. The correct option is (C).
The key idea here is that a diode does not obey Ohm’s law — its current-voltage relationship is exponential. So when we talk about “forward bias resistance,” we don’t mean a fixed resistance like in a resistor. Instead, we mean the dynamic resistance (also called AC resistance or small-signal resistance), which tells you how much the current changes for a small change in voltage around a given operating point.
Why does this matter? Because in exam problems like this, they give you a change in voltage and the corresponding change in current — that’s exactly the definition of dynamic resistance:
rd=ΔIΔV
Let’s apply it step by step.
-
Identify the given data
Initial voltage: V1=0.8 V
Final voltage: V2=1.0 V
Change in voltage: ΔV=V2−V1=1.0−0.8=0.2 V
Change in current: ΔI=2.0 mA=2.0×10−3 A
-
Apply the formula for dynamic resistance
rd=ΔIΔV=2.0×10−30.2
- Calculate rd=0.0020.2=100 Ω …
-
- CBSE 2023Set ANNUAL1 markMCQQ.On increasing the forward voltage of a forward biased p-n junction diode, its junction resistance :(a) increases(b) decreases(c) remains unchanged(d) None of these
›Reveal solutionSolution
Increasing the forward voltage decreases the junction resistance of a diode.
Under forward bias the depletion region narrows and the current rises steeply and non-linearly with voltage. Because the current increases faster than the voltage, the dynamic (junction) resistance dV/dI keeps falling as the forward voltage ri …
- CBSE 2018Set ANNUAL1 markQ.Find the current i in the circuit given below. Given, forward resistance of the diode is rf=1Ω, R=2Ω and V=10 volts.
›Reveal solutionSolution
Two diodes stacked in opposite (anti-parallel) directions between the same pair of nodes mean that whichever way current tries to flow through that pair, one of the two always blocks it — so the branch carries no current regardless of the applied EMF.
Circuit description
The battery V drives current through resistor R on the bottom wire. This connects to a node from which two diodes are drawn between the same two nodes, but pointing in opposite directions to each other; a third diode is then in series on the way back to the battery.
Reasoning
…
🎓Unlock everything free for 14 days
- ✓Full step-by-step solutions
- ✓Concept-first explanations
- ✓Methods, shortcuts & mistakes
- ✓PYQ mapping + timed mock tests
Full access for 14 days. No credit card required.