Question

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

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

Answer 1

Answer: (C)

$26 \, \Omega$

Answer 2

$P = \frac{V^{2}}{R}$
$R_{b} = \frac{V^{2}}{P} = \frac{10000}{500} = 20\, \Omega$
$i = \frac{100}{R_{b}} = \frac{130}{R}$
$\frac{100}{20} = \frac{130}{R}$
$R = 26\,\Omega$