I-V Characteristics

I-V characteristics (current-voltage graphs) show the relationship between the current through a component and the potential difference across it. Different components produce different characteristic shapes, which reveal important information about how the component behaves in a circuit.

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Experimental Setup

To investigate the I-V characteristics of a component, use the following circuit:

Circuit description:

• A variable d.c. power supply (or a battery with a variable resistor/rheostat in series) provides a range of p.d. values.
• The component under test is connected in the circuit.
• A voltmeter is connected in parallel across the component (to measure p.d.).
• An ammeter is connected in series with the component (to measure current).
• The variable resistor is adjusted to change the p.d. across the component.
• To obtain negative values (reverse bias for a diode), reverse the connections to the power supply.

Exam Tip: The ammeter must be in series (it measures the current flowing through the component). The voltmeter must be in parallel (it measures the p.d. across the component). Getting these wrong is a common practical error.

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1. Ohmic Conductor (e.g., Wire at Constant Temperature)

Graph: A straight line through the origin.

Key features:

• Current is directly proportional to potential difference
• The gradient is constant → resistance is constant
• The graph is symmetrical — reversing the p.d. reverses the current with the same magnitude
• Obeys Ohm's law

Gradient of the I-V graph:

• Gradient = I/V = 1/R
• A steeper line means lower resistance (higher conductance)

Worked Example 1 — Reading an I-V Graph

An ohmic conductor produces a straight-line I-V graph. At V = 4.0 V, I = 0.20 A. Calculate the resistance.

Solution:

R = V/I = 4.0 / 0.20 = 20 Ω

Since it is ohmic, this resistance is the same at all values of V.

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2. Filament Lamp

Graph: A curved line through the origin, with the curve bending towards the voltage axis (current increases less steeply at higher voltages).

Key features:

• The graph passes through the origin
• At low voltages, the graph is approximately linear (nearly ohmic)
• At higher voltages, the curve flattens — current increases more slowly
• Resistance increases as current increases
• The graph is symmetrical about the origin (same shape in both directions)

Explanation: As current increases through the filament:

1. The filament heats up (electrical energy → thermal energy)
2. Lattice ions in the tungsten filament vibrate more vigorously
3. Free electrons collide more frequently with the vibrating lattice ions
4. Drift velocity decreases for a given p.d.
5. Resistance increases

At low currents, the filament is cool and behaves almost ohmically. As the current increases, the temperature rises significantly (a filament lamp operates at about 2500°C), causing a large increase in resistance.

Worked Example 2 — Filament Lamp Resistance

A filament lamp has the following I-V data:

V (V)	I (A)
1.0	0.50
2.0	0.80
4.0	1.10
6.0	1.30

Calculate the resistance at 1.0 V and at 6.0 V.

Solution:

At 1.0 V: R = V/I = 1.0 / 0.50 = 2.0 Ω

At 6.0 V: R = V/I = 6.0 / 1.30 = 4.6 Ω

The resistance has more than doubled, confirming that the filament lamp does not obey Ohm's law.

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3. Thermistor (NTC — Negative Temperature Coefficient)

Graph: A curve through the origin, bending towards the current axis (current increases more steeply at higher voltages).

Key features:

• The graph passes through the origin
• At higher voltages (and currents), the curve steepens
• Resistance decreases as the thermistor heats up
• At low currents, behaviour is approximately ohmic

Explanation: As current flows through an NTC thermistor:

1. The thermistor heats up due to I²R heating
2. More electrons gain enough thermal energy to escape their atoms and become free charge carriers
3. The number density of charge carriers (n) increases substantially
4. The increase in n outweighs the increased collision rate
5. Resistance decreases