Question

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

Answer 1

$\text{Step 1 : Equivalent resistance}$

Let $n$ be the number of resistors to be connected in parallel

Then, $R_1=R_2=......=R_n=R=176\Omega$

Now, $\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+.....\frac{1}{R_n}$

$\Rightarrow \frac{1}{R_{eq}}=\frac{n}{R_1}=\frac{n}{176}$

$\Rightarrow R_{eq}=176/n$ $....\left(1\right)$

$\text{Step 2 : Applying Ohm's law}$

$V=I{R}_{eq}$

$\Rightarrow 220=5R_{eq}$

$\Rightarrow 220=5\times 176/n$ $($Using Equation $\left(1\right))$

$\Rightarrow n=4$

Hence, four resistors are required.