### Chapter 3: Electricity

Q
##### Electricity

Question:

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

Let the number of resistances be $n$.

The equivalent resistance of the resistors when connected in parallel is given by,

$\frac{1}{R} = \frac{1}{176} + \frac{1}{176} + \frac{1}{176} ......n\ times$

$\frac{1}{R} = \frac{1 + 1 + 1 +.....n\ times}{176}$

$\frac{1}{R} = \frac{n}{176}$

$R = \frac{176}{n}\ \Omega$

It is given that,

$V = 220\ V$

$I = 5\ A$

Now, using Ohm’s law

$V = IR$

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

$\frac{176}{n} = \frac{220}{5}$

$n = \frac{176 \times 5}{220}$

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

$n = 4$

Hence, four resistance of 176 Ω is required to draw the 5 A current when connected across the 220 V line.

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