Two identical electric heaters each marked 1000 W 220 V are connected in series . This conbination is connected to an AC supply of 220 V . What will be their combined rate of heating? (Assume resistance of each heater remians contant

Options

A. ` 1000 W`
B. `2000 W`
C. `500 W`
D. `4000 W`

Answer

C

Explanation

Let the resistance of the two heaters be denoted by `R_(1) and R_(2)`, respectively. Then
` R_(1) = (V^(2))/(P_(1)) and R_(2) = (V^(2))/(P_(2)))`
If the resistance of the series combination is denoted by `R_(s)` and the corresponding power by `R_(s) = R_(1) + R_(2)`. So
`(V^(2))/( P_(s)) = (V^(2))/(P_(1)) + (V^(2))/(P_(2))`
or `P_(s) = (P_(1)P_(2))/(P_(1) + P_(2)) = ( 1000 xx 1000 )/(2000) = 500 W`