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.