Question

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

Answer 1

Step 1: Given data

Ohm's law gives the equivalent resistance of resistors linked in parallel for $x$ number of resistors of resistance $176\Omega$ as,

$$\begin{gathered} V=IR \\ R=\frac{V}{I} \end{gathered}$$

Here voltage, $V=220V$, current $I=5A$, $R$ is equivalent resistance of the combination.

Step 2: Calculations.

$$\begin{gathered} \frac{1}{R}=x\times \left(\frac{1}{176}\right) \\ R=\frac{176}{x} \end{gathered}$$

From Ohm's Law,

$$\begin{gathered} \frac{V}{I}=\frac{176}{x} \\ x=\frac{176\times 5}{220}=4 \end{gathered}$$

Therefore, to draw the needed quantity of current, four $176\Omega$ resistors are required.