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?

Answer 1

For one bulb:
Power $P = 10\ W$ and Potential difference $V = 220\ V$
Using the relation for $R$, we have
$𝑅=\frac {𝑉^2}{𝑃}$

$R=\frac {(220)^2}{10}$
$R= 4840 \ Ω$
Let the total number of bulbs be $x$.
Given that:
Current $I = 5 \ A$ and Potential Difference $V = 220 \ V$
According to Ohm’s law, $V = IR$
$𝑅=\frac 𝑉𝐼$

$R =\frac {220}{5}$
$R =44 \ Ω$
Now, for $x$ number of bulbs of resistance 176 Ω, the equivalent resistance of the resistors connected in parallel is 44 Ω.
$\frac {1}{44}= \frac {1}{4840}+ \frac {1}{4840}+ \frac {1}{4840}+..... \text {𝑡𝑜 \ 𝑥\ 𝑡𝑖𝑚𝑒𝑠}$

⟹$\frac {1}{44}= \frac {𝑥}{4840}$

⟹$𝑥=\frac {4840}{44}$
⟹ $x=110$

Therefore, 110 bulbs of 4840 Ω are required to draw the given amount of current.