A heater is designed to operate with a power of P \( 1000 \mathrm{~...

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A heater is designed to operate with a power of
P \( 1000 \mathrm{~W} \) in a \( 100 \mathrm{~V} \) line.

W combination with a resistance of \( 10 \Omega \) and a resistance \( R \), to a \( 100 \mathrm{~V} \) mains as shown in the figure. What will be the value of \( R \) so that the heater operates with a power of \( 62.5 \mathrm{~W} \) ?
(a) \( 15 \Omega \)
(b) \( 10 \Omega \)
(c) \( 5 \Omega \)
(d) \( 25 \Omega \)
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