Question

Six similar bulbs are connected as shown in the figure with a DC source of emf E, and zero internal resistance.
The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be:

• A. 4:9
• B. 9:4
• C. 1:2
• D. 2:1

Answer 1

The Correct Option is B

To find the ratio of power consumption by the bulbs in two different scenarios, we need to analyze the circuit configurations given in the problem.

1. Initial Setup (All Bulbs Glowing):
   • The circuit consists of 6 similar bulbs arranged in two parallel sections (A and B) with three bulbs each.
   • Each parallel section has 3 bulbs in series.
   • If the resistance of each bulb is R, the total resistance in each section is 3R.
   • Since the sections are parallel, the equivalent resistance R_1 of the entire circuit is: R_1 = \frac{3R \times 3R}{3R + 3R} = \frac{3R}{2}.
2. Power Consumption:
   • The power consumed is given by P = \frac{E^2}{R_1}, where E is the emf of the source.
   • Substituting R_1: P_1 = \frac{E^2}{\frac{3R}{2}} = \frac{2E^2}{3R}.
3. Modified Setup (Two from Section A and One from Section B Glowing):
   • The circuit now consists of 2 bulbs in section A and 1 bulb in section B.
   • For Section A, the resistance becomes 2R and for Section B, it is R.
   • The equivalent resistance R_2 of the modified circuit is: R_2 = \frac{2R \times R}{2R + R} = \frac{2R}{3}.
4. Power Consumption:
   • The power consumed in this configuration is: P_2 = \frac{E^2}{R_2} = \frac{E^2}{\frac{2R}{3}} = \frac{3E^2}{2R}.
5. Ratio of Power Consumption:
   • We need to find the ratio \frac{P_1}{P_2}: \frac{P_1}{P_2} = \frac{\frac{2E^2}{3R}}{\frac{3E^2}{2R}} = \frac{2}{3} \times \frac{2R}{3E^2} \times \frac{3E^2}{2R} = \frac{9}{4}.

Therefore, the ratio of power consumption by the bulbs when all are glowing to the modified setup is 9:4.