Answer :
Final answer:
The power consumed by a 100 W bulb connected in series with a 60 W bulb at 220 V is calculated using the resistance of each bulb and Ohm's Law, resulting in approximately 14 W for the d) 100 W bulb.
Explanation:
When two bulbs with different power ratings are connected in series, the power consumption of each bulb changes due to the shared voltage supply. The relationship between voltage, current, and resistance in determining the power consumed by an electric device is given by the equation P = V^2/R, where P is the power, V is the voltage, and R is the resistance. To solve for the power consumed by the 100 W bulb connected in series with a 60 W bulb at 220 V, we need to first calculate the resistance of each bulb from their rated power and voltage using R = V^2/P, and then find the total resistance in the series circuit.
For the 100 W bulb, R1 = (220 V)^2 / 100 W
= 484 ohms.
For the 60 W bulb,
R2 = (220 V)^2 / 60 W
= 806.67 ohms. The total resistance is Rtotal = R1 + R2
= 484 ohms + 806.67 ohms
= 1290.67 ohms.
The total current through the circuit is I = V / Rtotal
= 220 V / 1290.67 ohms
= 0.170 A.
Now, the power consumed by the 100 W bulb is P1 = I^2 * R1
= (0.170 A)^2 * 484 ohms
≈ 14 W.
Therefore, the 100 W bulb consumes about 14 W when connected in series with a 60 W bulb at 220 V.