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How many lamps rated $10 W$ can be connected in parallel with each other across the two wires of $220 V$ line if the maximum allowable current is $5 A$ ?

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212

230

400

110

answer is D.

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Detailed Solution

110

lamps rated

10 W

can be connected in parallel with each other across the two wires of

220 V

line if the maximum allowable current is

5 A

.
Given, Voltage

V = 220 V

,
Power

P = 10 W

We know that ,

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

………………. (i)
Where

R^{'}

represents the resistance.
Therefore equation (i) can be written,

∴ R' = \frac{V^{2}}{P}

…………………… (ii)
When we substitute the values in equation (ii), we get

R' = \frac{220^{2}}{10}

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

R' = \frac{48400}{10}

R' = 4840 Ω

…………………… (iii)
Ohm's law states that

V = IR

R = \frac{V}{I}

When we substitute the values, we get

R = \frac{220}{5}

R = 44 Ω

………………… (iv)
Each electric bulb's resistance,

R^{'} = 4840 Ω

(

R_{P}

) Resistances in parallel connection are known to be expressed as,

\frac{1}{R_{P}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \dots . x

times.

\Rightarrow \frac{1}{44} = \frac{1}{R'} \times x

\Rightarrow \frac{1}{44} = \frac{x}{R'}

\Rightarrow R' = 44 \times x

\Rightarrow 4840 = 44 \times x

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

= 110

As a result,

110

bulbs can be connected in parallel.

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