Question

How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?

Answer 1

Let total no. of resistors connected in parallel be ‘n’ so that total effective resistance be R.
We know that according to Ohm’s Law,
V = IR
Therefore, R = V/I = 220/5 = 44ohm
Now since n such resistors are connected in parallel,so
1/R = n/176
or, 1/44 = n/176
n = 176/44 = 4resistors
Thus 4 such resistors will be required to connected in parallel.

Answer 2

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Let the total no. of resistors = x

Given,

I = 5 A

V = 220 V

According to Ohm’s law,

V = IR

R = V/ I = 220/5 = 44Ω

Now for x number of resistors of resistance 176 Ω, the equivalent resistance of the resistors connected in parallel is 44 Ω.

1/44 = 1/176 + 1/176 + 1/176 .....χ times

1/44 = x / 176

=> x = 176/ 44

=> x = 4

Therefore, 4 resistors of 176 Ω are required to draw the given amount of current.

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