Question

Several electric bulbs designed to be used on a 220 v supplied line r rated 20 w how many bulbs can be connected with parallel in each other across two wires of 220 v line if maximum allowed current is 10 ampere

Answer 1

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$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,
Supply Voltage of bulb$V = 220\: V$

Power Rating of the bulb $P= 20\: W$

Maximum Allowable Current $I = 10\: A$

No. of Bulbs that can be connected in parallel = ?

Let No. of bulbs connected in parallel are n

$\underline{\large{\textbf{Step-1}}}$:
Find the total Resistance provided by the circuit when 'n' bulbs are connected in parallel ($R_{t}$)

Using Ohms Law,
$V = I \times R$

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

Substituting Values

$R_{t} = \frac{220}{10}$

$\implies R_{t} = 22\: \Omega$

$\underline{\large{\textbf{Step-2}}}$:
Find the Resistance provided by each bulb $R_{b}$

We have,
$P = V \times I$

$\implies P= V × \frac{V}{R}$

$\implies P = \dfrac{V^{2}}{R}$

$\implies R = \dfrac{V^{2}}{P}$

Let Resistance provided by each bulb be $R_{b}$

Substituting Values

$R_{b} = \dfrac{220^{2}}{20}$

$\implies R_{b} = \dfrac{48400}{20}$

$\implies R_{b} = 2420\: \Omega$

$\underline{\large{\textbf{Step-3}}}$:
Find the Number of bulbs that can be connected in Parallel.

We have,
Equivalent Resistance of Resistors connected in parallel, $R_{t}$

$\dfrac{1}{R_{eq}} = \frac{1}{R_{b}} + \frac{1}{R_{b}} + \frac{1}{R_{b}} + .............\underbrace{n\: times}$

$\implies \dfrac{1}{R_{t}} = n \times (\dfrac{1}{R_{b}})$

$\implies n = \dfrac{R_{b}}{R_{t}}$

Substituting Values

$\implies n = \dfrac{4840}{22}$

$\implies n = 220$

Therefore,
No. of bulbs that can be connected in Parallel across two wires if maximum allowable current is 5A, is $\underline{\large{220}}$

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