Question

Two 220-volt, 100-watt bulbs are connected first in series and then in parallel. Each time the combination is connected to a 220-volt a.c. supply line. The power drawn by the combination in each case respectively will be:

• A. 50 watt,100 watt
• B. 100 watt,50 watt
• C. 200 watt,150 watt
• D. 50 watt,200 watt

Answer 1

The Correct Option is D

To solve this problem, let's analyze each scenario separately: the series connection and the parallel connection.

1. Series Connection

When two bulbs are connected in series, the same current flows through each bulb. However, the voltage across each bulb will be different. For the given bulbs:

• The voltage across each bulb if they were in parallel is 220 V. Thus, when in series, the total voltage is divided across them, which means each bulb gets 110 V (since they are identical).
• The power consumed by each bulb (P) is given by the formula: P = \frac{V^2}{R} where V is the voltage across the bulb and R is the resistance.

From the power formula: P = IV, and P = I^2R, we conclude that R = \frac{220^2}{100}.

Let's calculate the resistance: R = \frac{220^2}{100} = 484 \, \Omega.

Since each bulb gets 110 V, the power for each bulb in series is: P = \frac{110^2}{484} = 25 \, \text{watts}.

Thus, the total power consumed by both bulbs in series is: 25 \, \text{watts} \times 2 = 50 \, \text{watts}.

2. Parallel Connection

In a parallel connection, each bulb gets the full line voltage of 220 V.

• The resistance per bulb, as calculated above, is 484 Ω.
• Power for each bulb is then calculated using the same original configuration: P = \frac{220^2}{484} = 100 \, \text{watts}.

Thus, the total power consumed in parallel is: 100 \, \text{watts} \times 2 = 200 \, \text{watts}.

Conclusion

The power drawn by the combination is 50 watts when the bulbs are connected in series and 200 watts when connected in parallel.

Therefore, the correct answer is: 50 watt, 200 watt.