Two heaters rated as (P$_{1}$, V) and (P$_{2}$, V) are connected in...

Question

Two heaters rated as (P$_{1}$, V) and (P$_{2}$, V) are connected in series across a dc source of 2 volt. The power consumed by the combination will be –

Accepted Answer

Resistance of each heater from its rating: $R_1=\dfrac{V^2}{P_1}$, $R_2=\dfrac{V^2}{P_2}$

In series (assuming reconnected across the same voltage $V$): $R=R_1+R_2=V^2\left(\dfrac{1}{P_1}+\dfrac{1}{P_2}\right)=\dfrac{V^2(P_1+P_2)}{P_1P_2}$

Power consumed:

$$P=\frac{V^2}{R}=\frac{P_1P_2}{P_1+P_2}$$

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