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?

• A. 110 Ω
• B. 580 Ω
• C. 220 Ω
• D. 50 Ω

Answer 1

The correct option is A

110 Ω

Resistance of each bulb, r = $\frac{V^2}{P}$ = $\frac{{220}^2}{10}$ = 4840 $\Omega$

Total resistance in the circuit, R = $\frac{220V}{5A}$ = 44 $\Omega$

Let n be the number of bulb (each of resistance r) to be connected in parallel to obtain a resistance R.

Clearly, $R_{net}$ = $\frac{r}{n}$ or n = $\frac{r}{R}$ = $\frac{4840\Omega }{44\Omega }$ = 110 $\Omega$