Question

A $100\text{watt}$ bulb working on $200\text{volt}$ and a $200\text{watt}$ bulb working on $100\text{volt}$ have

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

Answer 1

The correct option is D maximum current ratings in the ratio of $1:4$

Step 1: Resistance of $100W$ bulb

Given,

$P_1=100W,V_1=200V$

Then Resistance of $100W$ bulb,

$R_1\frac{V_1^2}{P_1}=\frac{200\times 200}{100}=400\Omega$


Step 2: Resistance of $200W$ bulb

Given,

$P_2=200W,V_2=100V$

Then Resistance of $200W$ bulb,

$R_2=\frac{V_2^2}{P_2}=\frac{100\times 100}{200}=50\Omega$


Step 3: Calculation of maximum current rating

Maximum current through $R_1$ ,

$i_1=\frac{V_1}{R_1}=\frac{200}{400}=\frac{1}{2}A$

Maximum current through $R_1$ ,

$i_2=\frac{V_2}{R_2}=\frac{100}{50}=2A$

$\therefore i_1:i_2=1:4$

Hence, option (b) is correct.