5.5 Looking at the total resistance of resistors wired in a parallel circuit

We know the p.d. is 12.0 V and we now know from (a) the total current flowing is 8.0 A.

So, we can calculate the effective total resistance of the two resistors wired in parallel,

again using Ohm's Law: V = IR, R = V/I = 12.0/8.0 = 1.5 Ω

Note:

(i) When two resistors are wired in parallel, their combined resistance is much less than when wired in series - in fact it is lower than the lowest individual resistance.

In the series circuit 34, the total resistance was 8 ohms, here in circuit 35 when the resistors are wired in parallel, it is only 1.5 ohms and less than any of the individual resistances (2 ohms and 6 ohms).

The water pipe analogy helps here - think of the water being able to pass through two pipes of similar diameter.

(ii) NOT ON THE current UK GCSE specifications?

(as far as I know), the formula to calculate the total resistance of resistors in parallel.

The reciprocal of the total resistance = the total of all the reciprocals of the individual resistances added together.

1/R_total = 1/R₁ + 1/R₂ ... etc.

e.g. for the example above a 2 ohm resistor was wired in parallel with a 6 ohm resistor:

1/R_total = 1/R₁ + 1/R₂

1/R_total = 1/2 + 1/6 = 4/6 = 2/3 = 1/1.5, so R_total = 1.5/1 = 1.5 Ω

and note that the total resistance is less than the smallest resistance in the circuit.