sketch the I–V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp

Published by Patrick Mutisya · 14 days ago

Cambridge A-Level Physics 9702 – Resistance and Resistivity

Resistance and Resistivity

Learning Objective

Sketch the I–V characteristics of:

  1. a metallic conductor at constant temperature,

  2. a semiconductor diode, and

  3. a filament lamp.

Key Concepts

  • Ohm’s law for a linear resistor: \$V = IR\$.

  • Resistivity \$\rho\$ relates resistance to geometry: \$R = \rho \frac{L}{A}\$ where \$L\$ is length and \$A\$ is cross‑sectional area.

  • Temperature dependence:

    • Metals: \$R = R0[1+\alpha (T-T0)]\$ (positive temperature coefficient).

    • Semiconductors: \$R\$ decreases with temperature (negative temperature coefficient).

    • Filament lamps: \$R\$ rises sharply as the filament heats.

  • Non‑linear devices:

    • Diode current–voltage relation: \$I = IS\left(e^{\frac{qV}{kT}}-1\right)\$ where \$IS\$ is the saturation current.

    • Filament lamp: \$V\$ increases faster than \$I\$ because \$R\$ increases with temperature.

I–V Characteristics

1. Metallic Conductor (Constant Temperature)

At a fixed temperature the conductor obeys Ohm’s law, giving a straight line through the origin with slope \$1/R\$.

Suggested diagram: Linear I–V curve passing through the origin (positive slope).

2. Semiconductor Diode

The diode shows a highly non‑linear I–V curve:

  • In reverse bias, a tiny leakage current (approximately \$-I_S\$) flows.

  • In forward bias, current rises exponentially after the “turn‑on” voltage (≈0.6 V for silicon).

Suggested diagram: Exponential rise in forward bias, near‑zero current in reverse bias, with a sharp knee at the turn‑on voltage.

3. Filament Lamp

The filament’s resistance increases with temperature, so the I–V curve is concave upwards:

  • At low voltage the filament is cool, resistance is low, and the curve is relatively steep.

  • As voltage increases, the filament heats, resistance rises, and the slope (dI/dV) decreases.

Suggested diagram: Curve starting steep near the origin and bending to become more horizontal as voltage increases.

Comparison Table

DeviceShape of I–V CurveMathematical FormTemperature Effect on Resistance
Metallic conductor (constant T)Straight line through origin\$V = IR\$Negligible (by assumption)
Semiconductor diodeExponential rise in forward bias, near‑zero reverse current\$I = I_S\!\left(e^{\frac{qV}{kT}}-1\right)\$Resistance decreases as \$T\$ rises (more carriers)
Filament lampConcave‑upward, steeper at low \$V\$, flatter at high \$V\$Implicit; \$R(T)\$ rises sharply with \$T\$Resistance increases strongly with \$T\$ (positive coefficient)

Practical Tips for Sketching

  1. Mark the origin (0 V, 0 A) for all three curves.

  2. For the metal, draw a straight line; label its slope as \$1/R\$.

  3. For the diode, indicate the reverse‑bias leakage region and the forward‑bias “knee” around 0.6 V.

  4. For the filament lamp, start with a steep slope near the origin and gradually reduce the slope as voltage increases.