Question

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

• A. 900 W
• B. 450 W
• C. 300 W
• D. 200 W
• E. 100 W

Answer 1

Answer: (D)

Let $ {{R}_{1}} $ and $ {{R}_{2}} $ be the resistances, then $ H=\frac{{{V}^{2}}}{R} $ $ \therefore $ $ {{R}_{1}}=\frac{{{(200)}^{2}}}{300},{{R}_{2}}=\frac{{{(200)}^{2}}}{600} $ In series, $ R={{R}_{1}}+{{R}_{2}}=\frac{{{(200)}^{2}}}{300}+\frac{{{(200)}^{2}}}{600} $ $ =\frac{{{(200)}^{2}}}{100}\left[ \frac{1}{3}+\frac{1}{6} \right] $ $ =200\,\Omega $ Heat output, $ H=\frac{{{V}^{2}}}{R}=\frac{{{(200)}^{2}}}{200}=200\,V $