Question

Two identical immersion heaters are to be used to heat water, in a large container. Which one of the following arrangement would heat the water faster,

(I) connecting the heaters in series with the main supply

(II) connecting the heaters in parallel with the main supply

Give reasons for your answer

Answer 1

Let V be the voltage applied and R be the resistance of the individual coil.

When in series, the equivalent resistance is, R _s = R + R = 2R

Current drawn is, I _s = V/R _s = V/2R

So, heat produced in time ‘t’ is,

H _s = I _s ² R _s t

=> H _s = (V/2R) ² (2R) t

=> H _s = V ² t/(2R)

When connected in parallel,

The equivalent resistance is, R _p = R/2

Current drawn is, I _p = V/(R/2) = 2V/R

Heat produced in time ‘t’ is, H _p = (2V/R) ² (R/2) t

=> H _p = 2V ² t/R

Thus, heat produced in the parallel combination is more.