Parallel circuits

In parallel circuits, electrical components are connected alongside one another, forming extra loops.

Circuit rules

An electron will not pass through every component on its way round the circuit. If one of the bulbs is broken then current will still be able to flow round the circuit through the other loop. If one bulb goes out, the other will stay on.

Current in parallel

Since there are different loops, the current will split as it leaves the cell and pass through one or other of the loops An ammeter placed in different parts of the circuit will show how the current splits:

Circuit containing a switch, ammeter and cell, all connected in series, and two lamps connected in parallel.

I_1 = I_2 + I_4 = I_3

This is when:

  • current (I) is measured in amps (A)

Potential difference in parallel

Circuit containing a switch, 6V battery and two 100 ohm resistors in parallel. Label 1 points to a voltmeter connected across the battery, marked Vs. Labels 2 and 3 point to voltmeters connected across each resistor, marked V1 and V2 respectively.

Since energy has to be conserved, the energy transferred around the circuit by the electrons is the same whichever path the electrons follow.

The energy from the battery store is shared between the components depending on the resistance of each one.

Since potential difference is used to measure changes in energy, the potential difference supplied is equal to the potential differences across each of the parallel components but the value of current and resistance could be different.

The diagram shows a special case where both components have the same resistance and current and share the energy equally:

V_s = V_1 = V_2

This is when:

  • potential difference (V) is measured in volts (V)

Resistance in parallel

If two resistors are connected in parallel so that the current will flow through either one or the other, but not both, then the overall resistance is reduced as less current is flowing through each.

curriculum-key-fact
In parallel circuits:
  • the total current supplied is split between the components on different loops
  • potential difference is the same across each loop
  • the total resistance of the circuit is reduced as the current can follow multiple paths

Resistance in parallel - Higher

It is possible to use a formula to work out the total resistance of two resistors in parallel.

This is the formula:

\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}

It can be rearranged into a more useful form:

R_{total} = \frac{R_1 . R_2}{R_1 + R_2}

Examples

1. What is the total resistance of a 6 Ω and a 3 Ω resistor connected in parallel?

R_T = (6 \times 3) \div (6 + 3) = 18 \div 9 = 2~ \Omega

2. What is the total resistance of two 10 Ω resistors connected in parallel?

R_T = (10 \times 10) \div (10 + 10) = 100 \div 20 = 5~ \Omega