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ICSE Class 10 Physics Question 26 of 31

Current Electricity — Question 2

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Question

Question 2

Two lamps, one rated 220 V, 50 W and the other rated 220 V, 100 W, are connected in series with mains of voltage 220 V. Explain why does the 50 W lamp consume more power.

Answer

Resistance of lamp A (rating 220 V, 50 W) is —

RA=V2PAR_A = \dfrac{V^2}{P_A}

Substituting the values in the formula above we get,

RA=220250⇒RA=968ΩR_A = \dfrac{220^2}{50} \\[0.5em] \Rightarrow R_A = 968 Ω

Resistance of lamp B (rating 220 V, 100 W) is —

RB=V2PBR_B = \dfrac{V^2}{P_B}

Substituting the values in the formula above we get,

RB=2202100⇒RB=484ΩR_B = \dfrac{220^2}{100} \\[0.5em] \Rightarrow R_B = 484 Ω

From formula, we get, P = I2 R

As we observe that RA > RB and same current is flowing in both the lamps as both are connected in series therefore PA > PB. Hence, 50 W lamp consumes more power than 100 W lamp.