Two electric bulbs whose resistances are in the ratio 1:3 are connected in parallel to a constant voltage source. The powers dissipated in them have the ratio

Options

A. ` 1:3`
B. ` 1:1`
C. `3:1`
D. `1:9 `

Explanation

To solve the problem of finding the ratio of powers dissipated in two electric bulbs connected in parallel, we can follow these steps:

### Step 1: Understand the Given Information
We have two electric bulbs with resistances in the ratio of 1:3. Let's denote the resistances as:
- \( R_1 = R \) (for the first bulb)
- \( R_2 = 3R \) (for the second bulb)

### Step 2: Use the Power Formula
In a parallel circuit, the voltage across each component is the same. The power \( P \) dissipated in a resistor can be calculated using the formula:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage across the resistor and \( R \) is the resistance.

### Step 3: Write the Power Equations for Each Bulb
Using the power formula for both bulbs:
- For the first bulb:
\[ P_1 = \frac{V^2}{R_1} = \frac{V^2}{R} \]
- For the second bulb:
\[ P_2 = \frac{V^2}{R_2} = \frac{V^2}{3R} \]

### Step 4: Find the Ratio of Powers
To find the ratio of powers \( P_1 \) to \( P_2 \):
\[ \frac{P_1}{P_2} = \frac{\frac{V^2}{R}}{\frac{V^2}{3R}} = \frac{V^2}{R} \cdot \frac{3R}{V^2} = \frac{3R}{R} = 3 \]
Thus, the ratio of powers dissipated in the two bulbs is:
\[ P_1 : P_2 = 3 : 1 \]

### Conclusion
The ratio of the powers dissipated in the two electric bulbs is \( 3 : 1 \).

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