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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Thermal and Chemical Effects of Electric Current

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Thermal and Chemical Effects of Electric Current

When connected across a 220 V power supply, an electric bulb...

When connected across a 220 V220 \text{ V} power supply, an electric bulb consumes 60 W60 \text{ W} of power. What will be the power consumed if the supply voltage drops to 180 V180 \text{ V}, and what will it be if the supply is abruptly raised to 240 V240 \text{ V}?

Options

  1. A40 W40 \text{ W} and 71 W71 \text{ W}
  2. B33 W33 \text{ W} and 85 W85 \text{ W}
  3. C49 W49 \text{ W} and 65 W65 \text{ W}
  4. D50 W50 \text{ W} and 71 W71 \text{ W}

Correct answer

A. 40 W40 \text{ W} and 71 W71 \text{ W}

Step-by-step solution

The resistance of the electric bulb is given by R=V2PR = \dfrac{V^2}{P}

Substituting the given values, R=(220)260 ΩR = \dfrac{(220)^2}{60} \, \Omega

Assuming the resistance of the bulb remains constant, the power consumed at a new voltage V′V' is P′=(V′)2RP' = \dfrac{(V')^2}{R}

When the supply voltage drops to 180 V180 \text{ V}:

P1=(180)2(220)260=(180220)2×60=81121×60≈40.16 WP_1 = \dfrac{(180)^2}{\dfrac{(220)^2}{60}} = \left(\dfrac{180}{220}\right)^2 \times 60 = \dfrac{81}{121} \times 60 \approx 40.16 \text{ W}

When the supply voltage is raised to 240 V240 \text{ V}:

P2=(240)2(220)260=(240220)2×60=144121×60≈71.40 WP_2 = \dfrac{(240)^2}{\dfrac{(220)^2}{60}} = \left(\dfrac{240}{220}\right)^2 \times 60 = \dfrac{144}{121} \times 60 \approx 71.40 \text{ W}

The power consumed will be approximately 40 W40 \text{ W} and 71 W71 \text{ W}.
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