Two bulbs A and B are connected in parallel to a 3V source. If the ratio of resistance of bulb A to that of bulb B is 1:3. The ratio of the heat produced by bulb A to that of bulb B in a given time is:

Correct option is A

Sol: The correct answer is (a) 3:1

Given:

Voltage V=3V

Resistance ratio = $$\frac{R_A}{R_B} = \frac{1}{3}$$

Concept:

The power dissipated in an electrical component (which translates to the heat produced) can be determined using the formula:

P = $$\frac{V^2}{R}$$

Solution:

Resistance of bulb A as $$R_A$$​ and that of bulb B as $$R_B$$​​

From the resistance ratio:

​$$R_A$$ = R

$$R_B$$ = 3R

calculate the power (heat produced) for each bulb:

For bulb A

​$$P_A=\frac{V^2}{R_A}=\frac{3^2}{R}=\frac{9}{R}$$

​​For bulb B

​$$P_B=\frac{V^2}{R_B}=\frac{3^2}{3R}=\frac{9}{3R}=\frac{3}{R}$$

The ratio of the heat produced by bulb A to that of bulb B is

$$\frac{P_{A}}{P_{B}}=\frac{\frac{9}{R}}{\frac{3}{R}}=\frac{9}{3}=3:1$$

​​​So, the ratio of the heat produced by bulb A to that of bulb B is 3:1​