Two identical 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?
Two identical 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?
Let the voltage of the supply be V, resistance of the heater be ‘r’.
When connected in series the equivalent resistance is 2r and the current through each heater is, i = V/(2r)
So,
Heat developed in time ‘t’ by both the heater is, Hs = 2 × [V/(2r)]2(2r)t = V2t/r
When connected in parallel, the voltage across each heater is V and the current through each heater is i = V/r
So, the heat developed in time ‘t’ by both the heater is, Hp = 2 × (V/r)2(r)(t) = 2V2t/r
Thus, in parallel connection the heat developed is more for equal time interval.
So, water will heat faster on: (ii) Connecting the heaters in parallel with the main supply
Let the voltage of the supply be V, resistance of the heater be ‘r’.
When connected in series the equivalent resistance is 2r and the current through each heater is, i = V/(2r)
So,
Heat developed in time ‘t’ by both the heater is, Hs = 2 × [V/(2r)]2(2r)t = V2t/r
When connected in parallel, the voltage across each heater is V and the current through each heater is i = V/r
So, the heat developed in time ‘t’ by both the heater is, Hp = 2 × (V/r)2(r)(t) = 2V2t/r
Thus, in parallel connection the heat developed is more for equal time interval.
So, water will heat faster on: (ii) Connecting the heaters in parallel with the main supply
