AIPMT PRELIMS 2004 Physics Power in Electrical Circuits MCQ Question

To solve the problem of finding the power drawn by three identical bulbs of 60 watts, 200 volt rating when connected in series to a 200 volt supply, we need to understand how power, voltage, and resistance behave in series circuits.

Step 1: Determine the Resistance of Each Bulb

First, we can calculate the resistance of one bulb using the formula for power:

$$P = \frac{V^2}{R}$$

Where:

• $P$ is the power (in watts),
• $V$ is the voltage (in volts),
• $R$ is the resistance (in ohms).

For one bulb rated at 60 watts and 200 volts, we can rearrange the formula to find the resistance:

$$R = \frac{V^2}{P} = \frac{(200)^2}{60} = \frac{40000}{60} \approx 666.67 \, \Omega.$$

Step 2: Calculate the Total Resistance in Series

When the bulbs are connected in series, the total resistance $R_{total}$ is simply the sum of the individual resistances:

$$R_{total} = R_1 + R_2 + R_3 = R + R + R = 3R = 3 \times 666.67 \, \Omega \approx 2000 \, \Omega.$$

Step 3: Calculate the Total Current in the Circuit

Using Ohm's Law, we can find the current $I$ flowing through the circuit when connected to a 200 volt supply:

$$I = \frac{V_{supply}}{R_{total}} = \frac{200}{2000} = 0.1 \, A.$$

Step 4: Calculate the Total Power Drawn by the Bulbs

The total power $P_{total}$ drawn by the bulbs can be calculated using the formula:

$$P_{total} = I^2 R_{total}.$$

Substituting the values we found:

$$P_{total} = (0.1)^2 \times 2000 = 0.01 \times 2000 = 20 \, W.$$

Conclusion

Thus, the power drawn by the three bulbs when connected in series to a 200 volt supply is 20 watts.

Therefore, the correct option is C) 20 watt.

Explanation of Other Options

• A) 180 watt: This value is incorrect because it does not account for the series configuration of the bulbs. The total power in series is not simply additive as it would be in parallel.

• B) 10 watt: This is also incorrect. It underestimates the power based on the total resistance and current calculated.

• D) 60 watt: This is the power rating of a single bulb, not the total power consumed when they are connected in series. In series, the total power is based on the combined resistance and current flow.

Summary

In summary, the correct answer is C) 20 watt because, when connected in series, the total resistance increases, reducing the current and thus the overall power consumed by the circuit.