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A heater is designed to operate with a power of 1000 W on a line of 100 V. It is connected in combination with resistance of 10W and a resistance R to line of 100 V. The value of R so that the entire circuit operates with a power of 625 W is

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$5 Ω$

10 $Ω$

15 $Ω$

20 $Ω$

answer is C.

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Detailed Solution

Resistance of the heater is $R_{1} = \frac{100^{2}}{1000} = 10 Ω$

After joining the resistance the equivalent resistance of the whole circuit is $R_{2} = 10 + \frac{10 R}{10 + R}$

The power is given by $P' = \frac{V^{2}}{R_{2}} = 625 \Rightarrow R = 15 Ω$

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