In India electricity is supplied for domestic use at `220 V`. It is supplied at `110 V` in USA. If the resistance of a `60 W` bulb for use in India is `R`, the resistance of a `60 W` bulb for use in USA will be

Options

A. R/4
B. R/2
C. `R`
D. 2R

Answer

To find the resistance of a 60 W bulb for use in the USA, we can follow these steps:

### Step 1: Understand the relationship between power, voltage, and resistance
The power \( P \) of an electrical device is given by the formula:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage and \( R \) is the resistance.

### Step 2: Set up the equations for both countries
For the bulb used in India:
- Voltage \( V_1 = 220 \, V \)
- Power \( P = 60 \, W \)
- Resistance \( R_1 = R \)

Using the power formula:
\[ 60 = \frac{220^2}{R} \]
From this, we can express \( R \):
\[ R = \frac{220^2}{60} \]

For the bulb used in the USA:
- Voltage \( V_2 = 110 \, V \)
- Power \( P = 60 \, W \)
- Resistance \( R_2 = R' \)

Using the power formula again:
\[ 60 = \frac{110^2}{R'} \]
From this, we can express \( R' \):
\[ R' = \frac{110^2}{60} \]

### Step 3: Relate the resistances
Now we can relate the two resistances using the ratios of their voltages:
\[ \frac{R_1}{R_2} = \frac{V_1^2}{V_2^2} \]
Substituting the values:
\[ \frac{R}{R'} = \frac{220^2}{110^2} \]
Calculating the right side:
\[ \frac{R}{R'} = \frac{48400}{12100} = 4 \]
Thus, we can express \( R' \):
\[ R' = \frac{R}{4} \]

### Conclusion
The resistance of the 60 W bulb for use in the USA is:
\[ R' = \frac{R}{4} \]