Question

Two electric heater wires are made from the same material and have the same dimensions. First these are connected in series and then these are connected in parallel (to a 220 V AC source). Then the ratio of heat generated in the first case to the second case will be:

• A. 2 : 1
• B. 1 : 2
• C. 4 : 1
• D. 1 : 4

Answer 1

Answer: (D)

1 : 4

Let the two electric heater wires are connected to the supply E.

When both the wires are connected in series combination, the net resistance is:

$R_s=2R$

Heat generated in time $t$ is:

$H_s=\frac{E^2}{R_s}=\frac{E^2}{2R}.......\left(i\right)$

When both the wires are connected in parallel combination, the net resistance is:

$R_p=\frac{R}{2}$

Heat generated in time $t$ is:

$H_p=\frac{E^2}{R_p}=\frac{2E^2}{R}.....\left(ii\right)$

From (i) and (ii),

$\frac{H_s}{H_p}=\frac{1}{4}$