Ohm's Law and resistance

All conductors show some opposition to electrical current. This opposition to current is called resistance. There are several factors that affect the resistance of a conductor;

  • material, eg copper, has lower resistance than steel
  • length - longer wires have greater resistance
  • thickness - smaller diameter wires have greater resistance
  • temperature - heating a wire increases its resistance

The two main ways of increasing the current in an electrical circuit are by increasing the voltage or by decreasing the resistance.

Changing the voltage

If you increase the voltage across a component, there will be more current in the component. Too high a voltage and the lamp will break.

Three series circuits. The first has a cell, an ammeter reading 0.1 A and a lamp with a yellow glow. The second circuit has a double cell battery, an ammeter reading 0.2 A and a lamp with a brighter yellow glow. The third has a triple cell battery, an ammeter reading 0.3 A and a blown bulb.Three series circuits with increasing voltage

Changing the resistance

If you increase the number of lamps in a series circuit, there will be less current. The lamps resist current, so if you put more lamps into the circuit, there is more resistance.

Two series circuits. The first has a cell, a closed switch, a bright lamp and an ammeter reading 0.4 A . The second has a cell, closed switch, two dimmer lamps and an ammeter reading 0.2 A.Two series circuits, one with one lamp, the other with two

You could increase or decrease the resistance in a circuit by using a variable resistor.

Three series circuits, all containing a cell, ammeter, lamp and variable resistor. The first has an ammeter reading of 0.2 A and a dim lamp. The second has an ammeter reading of 0.4 A and a brighter lamp. The third has an ammeter reading of 0.5 A ammeter and an even brighter lamp.Three series circuits, all containing a cell, ammeter, lamp and variable resistor

The quantities voltage, current and resistance are linked by the relationship:

\[voltage = current \times resistance\]

This relationship is called Ohm's Law. We usually write Ohm's Law as;

\[V = IR\]

The symbol for resistance is R, it is measured in ohms \((\Omega )\).

The symbol for voltage is V, it is measured in volts \((V)\).

The symbol for current is I, it is measured in amperes \((A)\).

Make sure that if there is more than one voltage or current in a problem, you use the voltage across the resistor and the current through it, not just any values that you see in the question.

When a resistor is kept at a constant temperature, its resistance will remain unchanged. We can confirm this experimentally by connecting a resistor to a power supply and measuring the current in the resistor as the supply voltage is increased.

Plotting voltage (potential difference) against current for the resistor will produce a straight-line graph that passes through the origin.

Graph of potential difference (V) against current (A), showing a straight line running from origin to top right (positive)Graph of potential difference (V) against current (A)

A torch lamp takes a current of 0.3 amperes from a 3 volt battery. Calculate its resistance.

\[V = IR\]

\[3 = 0.3 \times R\]

\[R = \frac{3}{{0.3}}\]

\[R = 10\Omega\]

\[R=10 ohms\]


Calculate the reading on the ammeter in the circuit shown

Circuit with 12V power supply, ammeter resistor with 2.7 x 10 to the power of 3 Ohms and a voltmeter connected in parrallel.

\[I =\frac{V}{R}\]

\[=\frac{12}{2.7 \times 10^{3}}\]

\[= 4.4 \times 10^{-3}A\]

\[I = 4.4 \times 10^{-3}A\]

A change in temperature can cause a change in resistance for some materials. These materials are known as non-ohmic conductors.

For example, a thermistor’s resistance depends on its temperature.

A voltage-current graph for a thermistor is not a straight line.

Graph of voltage (V) against current (A). The line curves upwards before the rate of change decreases.voltage - current graph for a thermistor

This means that the resistance of the thermistor is not constant for different values of current. When the current decreases, the resistance of the thermistor increases.