Electrical power and I-V characteristicsEdexcel A-Level Physics: Revision notes

Power is the rate of energy transfer, and for an electrical component P = VI (watts = volts × amperes). The energy transferred in time t is W = VIt, which is just W = Pt.

Combining with V = IR gives two more forms:

• P = I²R (best when the current is the same, e.g. components in series)
• P = V²/R (best when the p.d. is the same, e.g. components in parallel or across a fixed supply)

Worked example: a 230 V, 2.3 kW kettle draws I = P/V = 2300/230 = 10 A. Its element has R = V²/P = 230²/2300 = 23 Ω. In 3.0 minutes it transfers W = 2300 × 180 = 4.1 × 10⁵ J.

An I–V characteristic plots current (y-axis) against p.d. (x-axis) for a component. The resistance at any point is R = V/I at that point.

For a straight line through the origin, the gradient is 1/R. For a curve, you must work out V/I at the point you are interested in. Do not use the gradient of a tangent as 1/R for a curved characteristic.

Always say whether the gradient is increasing or decreasing, then link it to what happens to resistance. A steeper line on an I–V graph means a lower resistance.

An ohmic conductor (e.g. a metal wire at constant temperature) gives a straight line through the origin: I ∝ V, constant resistance. This is Ohm's law, and it only holds if the temperature stays constant.

A filament lamp gives a curve whose gradient decreases as p.d. rises, so resistance increases. The current heats the tungsten filament, so the metal ions vibrate with greater amplitude. Conduction electrons collide with the ions more often, lowering their drift velocity for the same p.d.

Both characteristics are symmetrical about the origin when the p.d. is reversed.

A negative temperature coefficient (NTC) thermistor is a semiconductor whose resistance falls as its temperature rises. Heating releases more electrons from atoms, so the number of conduction electrons per unit volume (n) increases. This outweighs the extra lattice vibrations.

On an I–V graph, as p.d. and current rise the thermistor warms, its resistance falls and the curve becomes steeper.

At a fixed p.d., P = V²/R means falling resistance gives rising power and further heating. This positive feedback (thermal runaway) is why thermistors are often used with a series resistor.

A diode conducts in one direction only. In the forward direction the current is almost zero until the p.d. reaches a threshold (about 0.6–0.7 V for silicon), then rises steeply and the resistance becomes very small.

In the reverse direction the current is almost zero (very high resistance) up to a large breakdown p.d.

Worked example: a silicon diode (0.70 V) in series with a 220 Ω resistor and a 6.0 V battery: p.d. across resistor = 5.3 V, so I = 5.3/220 = 0.024 A. Reversed, I ≈ 0 and almost all 6.0 V is across the diode.