### Chapter 3: Electricity

Q
##### Electricity

Question:

Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A?

The resistance of each bulb $R$ can be calculated using the relation,

$P = \frac{V^2}{R}$

$R = \frac{V^2}{P}$

It is given,

$P = 10\ W$

$V = 220\ V$

$R = \frac{(220)^2}{10}$

$R = \frac{220 \times 220}{10}$

$R = 4840\ \Omega$

So, the resistance of each bulb is 4840 $\Omega$.

Let the number of lamps be $x$.

When lamps are connected in parallel, the equivalent resistance $R_{eq}$ will be,

$\frac{1}{R_{eq}} = \frac{1}{4840} + \frac{1}{4840} + \frac{1}{4840} -----x\ times$

$\frac{1}{R_{eq}} = \frac{1 + 1 + 1 + ----x\ times}{4840}$

$\frac{1}{R_{eq}} = \frac{x}{4840}$

$R_{eq} = \frac{4840}{x}-------(1)$

$V = 220\ V$ {Given}

$I = 5\ A$ {Given}

Using ohms law,

$V = IR_{eq}$

$R_{eq} = \frac{V}{I}$

$R_{eq} = \frac{220}{5}$

$R_{eq} = 44\ \Omega$

Putting the value of $R_{eq}$ in equation (1), we get

$44 = \frac{4840}{x}$

$x = \frac{4840}{44}$

$x = 110$

Therefore, 110 electric bulbs are connected in parallel.

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