If electric bulbs having resistances in the ratio 2 : 3 are connected in parallel to a voltage sources of 220 V. The ratio of the power dissipated in them is

Options

A. 2: 3`
B. 3 : 2 `
C. 1 : 1 `
D. 2: 5 `

Answer

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

### Step 1: Understand the Problem
We have two electric bulbs with resistances in the ratio of 2:3. They are connected in parallel to a voltage source of 220 V. We need to find the ratio of the power dissipated in these bulbs.

### Step 2: Assign Resistance Values
Let the resistance of the first bulb (R1) be 2x and the resistance of the second bulb (R2) be 3x, where x is a common factor.

### Step 3: Use the Power Formula
The power dissipated in a resistor when connected to a voltage source can be calculated using the formula:
\[ P = \frac{V^2}{R} \]
where P is the power, V is the voltage across the resistor, and R is the resistance.

### Step 4: Calculate Power for Each Bulb
Since the bulbs are connected in parallel, the voltage across both bulbs is the same (220 V).

- For the first bulb (R1):
\[ P_1 = \frac{V^2}{R_1} = \frac{(220)^2}{2x} = \frac{48400}{2x} = \frac{24200}{x} \]

- For the second bulb (R2):
\[ P_2 = \frac{V^2}{R_2} = \frac{(220)^2}{3x} = \frac{48400}{3x} \]

### Step 5: Find the Ratio of Power
Now, we can find the ratio of the power dissipated in the two bulbs:
\[ \frac{P_1}{P_2} = \frac{\frac{24200}{x}}{\frac{48400}{3x}} \]

This simplifies to:
\[ \frac{P_1}{P_2} = \frac{24200 \cdot 3x}{48400 \cdot x} = \frac{72600}{48400} = \frac{726}{484} = \frac{3}{2} \]

### Step 6: Conclusion
Thus, the ratio of the power dissipated in the two bulbs is:
\[ P_1 : P_2 = 3 : 2 \]