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  • A heater is designed to operate with a power of 1000W on a line of 100 V. It is connected in combination with resistance of 10Ω and a resistance R to line of 100 V. the value of R s

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

Option: 1

5 \Omega


Option: 2

10 \Omega


Option: 3

15 \Omega


Option: 4

20 \Omega


Answers (1)

best_answer

Power of the heater P= 1000 \mathrm{~W}

Potential difference V= 100 \mathrm{~V}

Therefore, resistance    \mathrm{R_1=\frac{V^2}{P}=\frac{100 \times 100}{1000}=10 \Omega}

Now resistance of the circuit is

\mathrm{R_2=10+\frac{10 R}{10+R}=\frac{100+20 R}{10+R} }

Therefore, power = \mathrm{\frac{V^2}{R_2}=625 \mathrm{~W} }

\mathrm{R_2=\frac{V^2}{625} \Rightarrow \frac{100+20 R}{10+R}=\frac{625}{100 \times 100} \Rightarrow R_2=15 \Omega }

Posted by

Pankaj

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