Curriculum

OCR A Level Physics A H556

1. Development of Practical Skills in Physics

0/56

2. Foundations in Physics

0/29

3. Forces and Motion

0/108

4. Electrons, Waves and Photons

0/71

OCR H556 chapter questions and answers

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Text lesson

4.2.2 Ohm’s Law and I-V Characteristics

4.2.2 Ohm’s Law and I-V Characteristics — OCR A Level Physics A notes: Define resistance, state Ohm’s law, and interpret the I-V characteristics of a resistor, filament lamp, diode and thermistor.

The resistance R of a component is the ratio of the potential difference V across it to the current I through it: R = V / I, with R in ohms (Ω), V in volts (V) and I in amperes (A).

One ohm is one volt per ampere.

A high resistance means a small current for a given p.d.

Resistance arises from collisions between the drifting charge carriers and the vibrating lattice ions.

Note that R = V/I defines the resistance at each point, whether or not the ratio is constant.

Conductance G = 1/R is measured in siemens (S).

Ohm’s law states that the current through a conductor is directly proportional to the potential difference across it, provided the temperature and other physical conditions remain constant.

Ohmic

A component that obeys it is ohmic: its I–V graph is a straight line through the origin, and its resistance is constant.

For such a graph with I on the y-axis, the gradient is 1/R, so a steeper line means a smaller resistance.

If axes are swapped (V on y), the gradient is R.

A metal wire at constant temperature is ohmic.

Many devices are non-ohmic: the current is not proportional to the p.d. In those cases the resistance at a point is found as V/I at that point, not as the gradient of the curve (the gradient of a tangent is not R unless the line passes through the origin).

I–V characteristics

Fixed resistor

Fixed resistor straight line through the origin, symmetric for reversed current. Ohmic.

Filament lamp

Filament lamp the curve flattens as V increases, in both directions (an S-shape through the origin). As the current rises the filament gets very hot, the lattice vibrates more and collisions increase, so resistance rises. The ratio V/I increases with V. Non-ohmic.

Semiconductor diode

Semiconductor diode in forward bias almost no current flows until a threshold of about 0.6 V for silicon (about 2 V for an LED), then current rises rapidly; in reverse bias the current is almost zero (a very small leakage) until breakdown.

Resistance falls steeply as the forward current rises and is very high in reverse.
It allows current in one direction only.

NTC thermistor

NTC thermistor as current heats it, resistance falls, so the I–V curve gets steeper with increasing p.d.

LDR

LDR straight line at constant light level, steeper in brighter light.

An I–V graph that is a straight line through the origin shows constant resistance.

A curve means resistance changes.

For a filament lamp the curve bends toward the V axis, so R rises with V; for a thermistor it bends toward the I axis, so R falls.

To find the resistance of a lamp at 4.0 V, read the current at that point and divide: R = 4.0/I.

A common mistake is to use the gradient there.

Power dissipated in a resistor: P = IV = I²R = V²/R, in watts. This heating (Joule heating) is why the temperature of the lamp filament rises. For ohmic resistors, P is proportional to V².

What the symbols mean: P = power (W) · I = current (A) · V = potential difference (V)

In a metal at constant temperature the drift velocity is proportional to the applied field because the average time between collisions is constant.

Link to the microscopic model

Using I = nAvq, I is then proportional to V and the resistance is constant.

In a filament, the temperature rises so collisions are more frequent and the drift velocity per unit field is smaller, giving the bend.

In a diode and a thermistor, the number density n of carriers changes with voltage or temperature, so resistance changes.

The power relations P = IV, P = I²R and P = V²/R apply to any component.

For a fixed resistor at constant R, doubling the current quadruples the power.

For a lamp, R rises with current so the power rises less quickly than I².

The energy transferred in time t is W = Pt = IVt.

Questions often ask why a lamp is most likely to fail at the moment of switching on: when cold its resistance is low, so the initial current is high and the heating is greatest.

Worked example 1. A resistor carries 0.25 A when the p.d. across it is 6.0 V. Find its resistance and the power dissipated.

R = V/I = 6.0/0.25 = 24 Ω.

P = IV = 0.25 × 6.0 = 1.5 W.

Worked example 2. A filament lamp passes 0.50 A at 3.0 V and 0.80 A at 9.0 V. Calculate its resistance at each point and explain the change.

R = 3.0/0.50 = 6.0 Ω; R = 9.0/0.80 = 11.3 Ω.

The filament is hotter at higher p.d., so the ions vibrate more, collisions increase, and the resistance rises.

Worked example 3. The I–V graph of a component is a straight line through (0,0) and (4.0 V, 20 mA). Find its resistance.

Gradient = 0.020/4.0 = 5.0 × 10⁻³ S, so R = 1/gradient = 200 Ω.

Term	Meaning
Resistance	R = V/I, in ohms.
Ohm’s law	I ∝ V for a conductor at constant temperature.
Ohmic conductor	Conductor with constant resistance, a straight I–V line through the origin.
I–V characteristic	Graph of current against p.d. for a component.
Threshold voltage	Forward p.d. above which a diode conducts significantly.
Conductance	G = 1/R, in siemens.

Saying Ohm’s law is V = IR for every component. It is a statement about proportionality at constant temperature.

Taking resistance as the gradient of a curved I–V graph.

Forgetting that a diode conducts only in forward bias above a threshold.

Mixing the axes: with I on the y-axis, gradient = 1/R.

Saying resistance rises for all components when heated; thermistors fall.