Question

A filament bulb ($500W,100V$) is to be used in a $230V$ main supply. When a resistance $R$ is connected in series, it works perfectly and the bulb consumes $500W$. The value of $R$ is

• A. $26\Omega$
• B. $13\Omega$
• C. $230\Omega$
• D. $46\Omega$

Answer 1

The correct option is A $26\Omega$


As in first case there is no resistance except the bulb so, the resistance of the bulb can be calculated as,
$R_{bulb}=\frac{V^2}{P}=\frac{{100}^2}{500}=20\Omega$
In second case the bulb and the resistance are in series, current remains same across them and the resistance of the bulb is also same, by using ohm's law $V\propto R$
$\frac{R}{R_{bulb}}=\frac{130}{100}\Rightarrow \frac{R}{20}=\frac{130}{100}\Rightarrow R=26\Omega$