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Question
What is the resistance, under normal working conditions, of an electric lamp rated at '240 v, 60 W' ? If two such lamps are connected in series across a 240 V mains supply, explain why each one appears less bright.
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Solution
Given voltage, V = 240 V
Power, P = 60 W
As P = `"V"^2/"R"`
∴ R = `(240)^2/60`
= 960 Ω
I = `"P"/"V"` = 0.25 A
When one lamp is connected across the mains, it draws 0.25 A current, while if two lamps are connected in series across the mains, current through each bulb becomes
`(240 "V")/((960 + 960) Omega) = 0.125 "A"`
(i.e., current is halved), hence heating (= I2Rt) in each bulb becomes one-fourth, so each bulb appears less bright.
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