Question

two identical immersion heaters are to be used to heat water,in large container.Which one of th efollowing arrangementt would heat the water faster:a)connecting the heaters in series with the main supply, b)connecting the heaters in parallel with the main supply?give reasons

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.