A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of 10 ? and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be _____

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Solution

Q.
A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of 10 Ω and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be _____ $Ω$ . [2024]

Ans.
(5)

$R_{heater} = \frac{V^{2}}{P} = \frac{{(100)}^{2}}{1000} = 10 Ω$

For heater $P = \frac{V^{2}}{R} \Rightarrow V = \sqrt{P R}$

$V = \sqrt{62.5 \times 10} = 25 V$

$i_{1} = \frac{75}{10} = 7.5 A, i_{H} = \frac{25}{10} = 2.5 A$

$i_{R} = i_{1} - i_{H} = 7.5 - 2.5 = 5 A$

$V = I R \Rightarrow R = \frac{25}{5} = 5 Ω$

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