Discussion
A 100-Watt, 200 Volts lamp is connected in series with a second lamp of 100 Watt, 150 Volts across a 250 Volts supply. Find the voltage across the second lamp.
Answer: A
The resistance of a lamp is \(V^2/P\). The first lamp has \(200^2/100 = 400\ \Omega\) and the second \(150^2/100 = 225\ \Omega\). In series the total resistance is 625 ohm and the current is \(250/625 = 0.4\) A. The voltage across the second lamp is
\[ V_2 = 0.4 \times 225 = 90\ \text{V} \]The first lamp then has 160 V across it. The options 100 V and 125 V would result from splitting the supply equally or in the ratio of the rated voltages, which is wrong because the lamps have different resistances; 160 V is the voltage across the first lamp, not the second.
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