Question

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

Answer 1

Step 1: Given Data

Current $I=5A$

Voltage $V=220V$

Resistance of each resistor $r=176\Omega$

Let the number of resistors in parallel be $n$.

Step 2: Formula Used

Resistance $R=\frac{V}{I}$

For $n$ number of resistors of resistance $r$ in parallel

$\frac{1}{R}=\frac{n}{r}$

Step 3: Calculate Equivalent Resistance

According to Ohm's law,

Resistance $R=\frac{V}{I}$

$$\begin{gathered} =\frac{220}{5} \\ =44\Omega \end{gathered}$$

Step 4: Calculate Number of Resistors

We know that $n$ resistors of resistance $r$ are in parallel to give an equivalent resistance of $R$.

$\therefore \frac{1}{R}=\frac{n}{r}$

$\Rightarrow n=\frac{r}{R}$

$\Rightarrow n=\frac{176}{44}=4$

Hence, four equal resistors are connected in parallel to the circuit.