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`
B. `2 R`
C. `(R )/(4)`
D. `(R )/(2)`

Explanation

To find the resistance of a 60 W bulb for use in the USA given that the resistance of a 60 W bulb for use in India is \( R \), we can use the relationship between power, voltage, and resistance.

### Step-by-Step Solution:

1. **Understand the Power Formula**:
The power \( P \) consumed by an electrical device can be expressed using the formula:
\[ P = \frac{V^2}{R} \]
where \( P \) is the power in watts, \( V \) is the voltage in volts, and \( R \) is the resistance in ohms.

2. **Set Up the Equation for India**:
For the 60 W bulb in India, the voltage supply is \( 220 \, V \). Therefore, we can write:
\[ 60 = \frac{220^2}{R} \]
Rearranging this gives:
\[ R = \frac{220^2}{60} \]

3. **Calculate the Resistance \( R \)**:
Now, calculate \( R \):
\[ R = \frac{48400}{60} = 806.67 \, \Omega \]

4. **Set Up the Equation for the USA**:
For the 60 W bulb in the USA, the voltage supply is \( 110 \, V \). Using the same power formula:
\[ 60 = \frac{110^2}{R_{USA}} \]
Rearranging gives:
\[ R_{USA} = \frac{110^2}{60} \]

5. **Calculate the Resistance \( R_{USA} \)**:
Now, calculate \( R_{USA} \):
\[ R_{USA} = \frac{12100}{60} = 201.67 \, \Omega \]

6. **Relate the Two Resistances**:
We know from the earlier calculations that:
\[ R_{USA} = \frac{R}{4} \]
Therefore, if \( R \) is the resistance of the bulb in India, the resistance of the bulb in the USA will be:
\[ R_{USA} = \frac{R}{4} \]

### Final Answer:
The resistance of a 60 W bulb for use in the USA will be \( \frac{R}{4} \).