If two electric bulbs have 40 W and 60 W rating at V 220 , then the ratio of their resistances will be

Options

A. `3 : 2`
B. `2 : 3`
C. `3 : 4`
D. `4 : 3`

Answer

To find the ratio of the resistances of two electric bulbs rated at 40 W and 60 W at a voltage of 220 V, we can follow these steps:

### Step-by-Step Solution:

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

2. **Write the equations for both bulbs**:
For the first bulb (40 W):
\[ P_1 = 40 \, \text{W} = \frac{(220 \, \text{V})^2}{R_1} \]
For the second bulb (60 W):
\[ P_2 = 60 \, \text{W} = \frac{(220 \, \text{V})^2}{R_2} \]

3. **Rearranging the equations to find resistance**:
From the power equations, we can express the resistances \( R_1 \) and \( R_2 \):
\[ R_1 = \frac{(220 \, \text{V})^2}{40 \, \text{W}} \]
\[ R_2 = \frac{(220 \, \text{V})^2}{60 \, \text{W}} \]

4. **Finding the ratio of the resistances**:
To find the ratio \( \frac{R_1}{R_2} \):
\[ \frac{R_1}{R_2} = \frac{\frac{(220 \, \text{V})^2}{40}}{\frac{(220 \, \text{V})^2}{60}} = \frac{60}{40} = \frac{3}{2} \]

5. **Conclusion**:
The ratio of the resistances \( R_1 : R_2 \) is \( 3 : 2 \).

### Final Answer:
The ratio of their resistances is \( 3 : 2 \).

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