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 a single bulb: Power \(P = 10\ W\) and Potential difference \(V = 220\ V\). Using the relation for \(R\), we get \(𝑅=\frac {𝑉^2}{𝑃}\). Substituting the values, \(R=\frac {(220)^2}{10} = 4840\ Ω\).
Let the total number of bulbs be \(x\). Given Current \(I = 5\ A\) and Potential Difference \(V = 220\ V\). According to Ohm’s law, \(V = IR\), so \(𝑅=\frac 𝑉𝐼\). Substituting the values, \(R =\frac {220}{5} =44\ Ω\).
Now, for \(x\) bulbs, each with a resistance of 4840 Ω, connected in parallel, the equivalent resistance is 44 Ω.
\(\frac {1}{44}= \frac {1}{4840}+ \frac {1}{4840}+ \frac {1}{4840}+..... \text { 𝑡𝑜 \ 𝑥 \ 𝑡𝑖𝑚𝑒𝑠}\)

This simplifies to \(\frac {1}{44}= \frac {𝑥}{4840}\).

Solving for \(x\): \(𝑥=\frac {4840}{44}\) which gives \(x=110\).

Therefore, 110 bulbs, each with a resistance of 4840 Ω, are required to draw a current of 5 A at a potential difference of 220 V.