Two heaters designed for the same voltage `V` have different power ratings. When connected individually across as source of voltage` V`, they produce `H` amount of heat each in time `t_1` and `t_2` respectively. When used together acros the same source, they produce H amount of heat in time t

Options

A. `t = t_(1) = t_(2)` If the beaters are in series
B. `t =2 (t_(1) + t_(2))` If the beaters are in series
C. `t = (t_(1)t_(2))/(t_(1) + t_(2))` If the heaters are in parallel
D. `t = (t_(1)t_(2))/(2(t_(1) + t_(2))` If the heaters are in parallel

Answer

a,c,d

Explanation

As `H = (V^(2))/(R ) t, R = (V^(2))/(H )t, R_(1) rarr (V^(2))/(H )t_(1),R_(2) = (V^(2))/(H )t_(2)`
(a) In series, `R = R_(1) + R_(2)`
or `(V^(2))/(H) t = (V^(2))/(H)t_(1) + (V^(2))/(H)t_(2) or t = t_(1) + t_(2)`
(c) in parallel `rarr (1)/(R ) = (1)/(R_(1)) + (1)/(R_(2))`
or `(H)/(V^(2)t) = (H)/(V^(2)t_(1)) + (H)/(V^(2)t_(2))`
`(1)/(t) = (1)/(t_(1)) + (1)/(t_(2)) or t = (t_(1)t_(2))/(t_(1) +t_(2))`