CBSE Class 10 Science 2018 · Paper 31(B) · Question 21

Electricity 5 marks Medium

(a)Derive an expression for the equivalent resistance of three resistors of resistance $R_{1}$ , $R_{2}$ and $R_{3}$ connected in series.
(b)Three fuse of rating 3A, 5A and 7A are available. Which one of these will be most suitable to operate an electric iron of 1 kW power at 220 V electric line ? Give reason to justify your answer.

Answer

In series $R_{s} = R_{1} + R_{2} + R_{3}$ ; the iron draws about $4.5$ A, so the 5 A fuse is the most suitable.

(a) In a series combination the same current

I

flows through each resistor, and the potential difference

V

across the combination is the sum of the potential differences across the individual resistors:

V = V_{1} + V_{2} + V_{3}

. By Ohm's law,

V_{1} = I R_{1}

V_{2} = I R_{2}

and

V_{3} = I R_{3}

. If

R_{s}

is the equivalent resistance,

V = I R_{s}

. So

I R_{s} = I R_{1} + I R_{2} + I R_{3}

, that is,

R_{s} = R_{1} + R_{2} + R_{3}

. (b) Current drawn by the iron:

I = \frac{P}{V} = \frac{1000 W}{220 V} \approx 4.5

A. The 5 A fuse is the most suitable: it carries the normal current of about

4.5

A without melting but melts if the current rises above 5 A. A 3 A fuse would melt as soon as the iron is switched on, since

4.5

A is more than 3 A, and a 7 A fuse would let an overload current of up to 7 A flow without melting, so it would not protect the iron and the wiring.

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