Physics - Current Electricity Question with Solution | TestHub

Power rating of heater, $\mathrm{P}=1000\mathrm{W}$ Voltage rating of heater, $\mathrm{V}=100\mathrm{V}$$\therefore$ Resistance of heater, ${\mathrm{R}}_1=\frac{{\mathrm{V}}^2}{\mathrm{P}}=\frac{(100{)}^2}{1000}=10\Omega$ According to question, power dissipated in heater, ${\mathrm{P}}^{\prime }=62.5\mathrm{W}$ $\therefore$ Voltage $({\mathrm{V}}^{\prime }$ ) across heater can be calculated as $\begin{array}{rl}& {\mathrm{P}}^{\prime }=\frac{{\left({\mathrm{V}}^{\prime }\right)}^2}{{\mathrm{R}}_1}\Rightarrow {\left({\mathrm{V}}^{\prime }\right)}^2={\mathrm{P}}^{\prime }\times {\mathrm{R}}_1=62.5\times 10\\ & \Rightarrow {\mathrm{V}}^{\prime }=25\mathrm{V}\text{ (across heater) }\\ & \end{array}$ $\therefore$ Voltage across $10\Omega$ resistor, ${\mathrm{V}}^{\prime \prime }=100-25=75\mathrm{V}$ Current in $10\Omega$ resistor $=\frac{{\mathrm{V}}^{\prime \prime }}{10}=\frac{75}{10}=7.5\mathrm{A}$ Current in heater resistor $=\frac{{\mathrm{V}}^{\prime }}{10}=\frac{25}{10}=2.5\mathrm{A}$ So, current in $\mathrm{R}\Omega =7.5-25=5\mathrm{A}$ Now, $\mathrm{V}=\mathrm{IR}\Rightarrow \mathrm{R}=\mathrm{V}/\mathrm{I}=\frac{25}{5}=5\Omega$