Sketch and explain the current-voltage graphs for a resistor of constant resistance, a filament lamp and a diode

Topic 4.2.4 – Resistance

Learning objectives

• Define electrical resistance and state its unit.
• State the quantitative relationship R = V ⁄ I and explain how it follows from Ohm’s law.
• Describe how the resistance of a uniform conductor depends on its length, cross‑sectional area and material (R ∝ L, R ∝ 1⁄A, ρ).
• Carry out a simple volt‑ammeter experiment to determine the resistance of an unknown resistor and interpret the resulting V‑I graph.
• Sketch and explain the current‑voltage (I‑V) graphs for:

  • a resistor of constant resistance,
  • a filament lamp,
  • a semiconductor diode.

Core concepts

Practical method – determining an unknown resistance

1. Connect the unknown resistor in series with a variable DC source, an ammeter (to measure I) and a voltmeter (to measure V across the resistor).
2. Vary the source voltage and record several (V, I) pairs.
3. Plot the points on a graph with V (V) on the horizontal axis and I (A) on the vertical axis.
4. If the resistor is ohmic the points lie on a straight line through the origin; the slope of the line is 1⁄R. Hence R = ΔV ⁄ ΔI.

1. Resistor of constant resistance (ohmic resistor)

An ideal metallic resistor obeys Ohm’s law over the range of voltages used in the IGCSE exam.

Graphical features

• Horizontal axis: Voltage, V (V)
• Vertical axis: Current, I (A)
• The line passes through the origin because I = 0 when V = 0.
• Slope = ΔI⁄ΔV = 1⁄R. A steeper slope indicates a lower resistance.

2. Filament lamp (non‑ohmic conductor)

A filament lamp is made of a metal (usually tungsten) whose resistance increases markedly as the filament temperature rises.

Why the I‑V curve bends

• At low voltage the filament is cool → small R → the initial part of the curve is almost linear.
• Increasing V raises the current, which heats the filament; R rises, so the incremental increase in I for a given increase in V becomes smaller.
• The result is a convex‑upward curve that flattens as V (and temperature) increase.

Typical experimental procedure

1. Connect the lamp to a variable DC source with an ammeter in series and a voltmeter across the lamp.
2. Record V and I for several settings, then plot I versus V.
3. The plotted points start at the origin and curve upward, never forming a straight line.

3. Semiconductor diode

A diode conducts readily in the forward direction but blocks current in reverse bias (apart from a tiny leakage current). Its I‑V characteristic has three distinct regions.

Graphical features

• Axes: V (V) horizontal, I (A) vertical.
• Region A: a near‑horizontal line close to the I = 0 axis (reverse‑bias leakage).
• Region B: a shallow, almost flat segment up to the “knee” voltage V_k.
• Region C: a steep upward curve. In IGCSE sketches this is often drawn as a straight line with a very steep slope, but the true relation is exponential:

    \(I = I_0\bigl(e^{qV/kT} - 1\bigr)\).

• Mark V_k on the graph (≈ 0.6 V for a silicon diode).

Comparative summary

Practical tips for sketching I‑V graphs

1. Label both axes clearly, including units (V (V) on the horizontal, I (A) on the vertical).
2. Start the graph at the origin for any device that carries zero current when the voltage is zero (resistor, filament lamp). For a diode the reverse‑bias line is drawn close to the I = 0 axis, not at the origin.
3. For an ohmic resistor draw a straight line; the slope equals 1⁄R.
4. When resistance changes with temperature or voltage, indicate the curvature qualitatively – exact numerical values are not required at IGCSE level.
5. For the diode, clearly mark the knee voltage V_k and note the typical value (≈ 0.6 V for silicon).

Common misconceptions

• “A filament lamp has a constant resistance.” In reality the filament’s resistance can increase 40–60 times as it heats.
• “The diode’s forward characteristic is a straight line.” The current rises exponentially; the straight‑line sketch is only a shorthand for “very steep”.
• “A reverse‑biased diode conducts a normal current.” Only a tiny leakage current flows until breakdown, which is outside the IGCSE syllabus.
• “Current can flow from cathode to anode.” In forward bias current flows from anode to cathode only.

Exam checklist

1. State the definition of resistance (R = V ⁄ I) and its unit.
2. Explain how R depends on length, area and material (R ∝ L, R ∝ 1⁄A).
3. Describe the volt‑ammeter method for finding an unknown resistance and indicate how the slope of the V‑I graph gives R.
4. Draw a straight‑line I‑V graph for a constant‑R resistor, label the axes and write “slope = 1⁄R”.
5. Sketch the curved I‑V graph for a filament lamp and give a one‑sentence explanation (temperature‑dependent increase in R).
6. Produce the three‑region I‑V graph for a diode, label the reverse‑bias region, the knee voltage (≈ 0.6 V for Si) and the steep forward region.
7. For each component, provide a concise physical reason for the shape of its graph.