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

Options

A. `9 : 4`
B. `4 : 3`
C. `3 : 8`
D. `3 : 2`

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 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 \(P\) is the power in watts, \(V\) is the voltage in volts, and \(R\) is the resistance in ohms.

### Step 2: Write the equations for both bulbs
For the first bulb (40 W):
\[ P_1 = \frac{V^2}{R_1} \implies R_1 = \frac{V^2}{P_1} \]
For the second bulb (60 W):
\[ P_2 = \frac{V^2}{R_2} \implies R_2 = \frac{V^2}{P_2} \]

### Step 3: Substitute the values into the equations
Given \(V = 220 V\), \(P_1 = 40 W\), and \(P_2 = 60 W\):
\[ R_1 = \frac{(220)^2}{40} \]
\[ R_2 = \frac{(220)^2}{60} \]

### Step 4: Find the ratio of the resistances
Now, we need to find the ratio \( \frac{R_1}{R_2} \):
\[ \frac{R_1}{R_2} = \frac{\frac{(220)^2}{40}}{\frac{(220)^2}{60}} = \frac{60}{40} = \frac{3}{2} \]

### Step 5: Conclusion
The ratio of the resistances of the two bulbs is:
\[ \frac{R_1}{R_2} = \frac{3}{2} \]