Question

A heater is designed to operate with a operator with a power of $1000W$ in a $100V$ line. It is connected to two resistance of $10\Omega$ and $R\Omega$ as shown in figure. If the heater is now operating with a power of $62.5W$. Calculate the value of $R\left(inohm\right)$

Answer 1

Resistance of heater,
$R^{\prime }=\frac{{100}^2}{1000}=10\Omega$
When heater is in the circuit, let potential difference across heater be V, then
$62.5=\frac{V^2}{10}\Rightarrow V^2=625$
$V=25volt$
Therefore, current through heater
$I_2=\frac{25}{10}=2.5A$
Voltage drop across $10\Omega$ resistor connected in series of the heater $=100-25=75volt$
Main current $=\frac{75}{10}=7.5A$
$\therefore$ Current through resistance $R=7.5-2.5=5A$
$\therefore$ Resistance $R=\frac{25}{5}=5\Omega$