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

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 Ω  (B) 46 Ω  (C) 26 Ω  (D) 13 Ω

Tardigrade Admin · Accepted Answer

P = (V2/R) Rb = (V2/P) = (10000/500) = 20 Ω i = (100/Rb) = (130/R) (100/20) = (130/R) R = 26 Ω

Q. 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

$230 Ω$

$46 Ω$

$26 Ω$

$13 Ω$

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

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

230Ω

46Ω

26Ω

13Ω