Question

A heater $A$ gives out 300 W of heat when connected to a 200 V d.c. supply. A second heater $B$ gives out 600 W when connected to a 200 v d.c. supply. If a series combination of the two heaters is connected to a 200 V d.c. supply the heat output will be

• A. 100 W
• B. 450 W
• C. 300 W
• D. 200 W

Answer 1

Answer: (D)

200 W

The two heaters with different power are connected in series,

$P1=\frac{V^2}{R1}$ and $P2=\frac{V^2}{R2}$

therefore,

$R1=\frac{V^2}{P1}$ and $R2=\frac{V^2}{P2}$

in series combination

$R_{eq}=R1+R2$

Hence,

$P_{eq}=\frac{V^2}{P1}+\frac{V^2}{P2}$

$P_{eq}=\left(\frac{1}{2}\right)V^2$

$P_{eq}=\frac{1}{2}\left(400\right)=200W$