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

Current Electricity

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Answer

Given,

I = 5 A

V = 220 V

Let number of resistors be n

Resistance of each resistor = 176 Ω

1Req=1176+1176+....n1Req=n176Ω⇒Req=176nΩ\dfrac{1}{\text{R}{eq}} = \dfrac{1}{176} + \dfrac{1}{176} + ….n \\[1em] \dfrac{1}{\text{R}{eq}} = \dfrac{\text{n}}{176} \Omega \\[1em] \Rightarrow \text{R}_{eq} = \dfrac{176}{\text{n}} \Omega

Applying Ohm's Law:

V = IR

220 = 5 x 176n\dfrac{176}{\text{n}}

n = 176×5220\dfrac{176 \times 5}{220} = 4 resistors

Hence, 4 resistors are connected in parallel.

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