Question

A 100 watt bulb working on 200 volt and a 200 watt bulb working on 100 volt have

• A. Resistances in the ratio of 4 : 1
• B. Maximum current ratings in the ratio of $1:4$
• C. Resistances in the ratio of 2 : 1
• D. Maximum current ratings in the ratio of 1 : 2

Answer 1

Answer: (B)

Maximum current ratings in the ratio of $1:4$

Answer 2

$R = \frac{V^{2}}{P}$ ⇒ $R_{1} = \frac{200 \times 200}{100} = 400\Omega$ and

$R_{2} = \frac{100 \times 100}{200} = 50\Omega.$

Maximum current rating$i = \frac{P}{V}$

So $i_{1} = \frac{100}{200}$ and$i_{2} = \frac{200}{100}$⇒ $\frac{i_{1}}{i_{2}} = \frac{1}{4}$.