Q.

You are given several identical resistances each of value R = 10Ω and each capable of carrying maximum current of 1 ampere. It is required to make a suitable combination of these resistances to produce a resistance of 5Ω  which can carry a current of 4 amperes. The minimum number of resistances of the type  R that will be required for this job

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a

4

b

10

c

8

d

20

answer is C.

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Detailed Solution

Suppose n resistors are used for the required job. Suppose equivalent resistance of the combination is R' and according to energy conservation its current rating is  i'.Energy consumed by the combination = n x (Energy consumed by each resistance)⇒i'2R′=n×i2R⇒n=i′i2×R′R=412×510=8
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