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Several electric bulbs designed to be used on a 220V electric supply line, are rated 10W. How many lamps can be connected in parallel with each other across the two wires of 220V line, if the maximum allowable current is 5A ? |
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Answer» Given: V = 220 V Power of each bulb, P = 10 W Current, I = 5 A Let the number of bulbs = n. We have, R = \(\frac{V^2}{P}\) = \(\frac{220 \times \ 220}{10}\) = 4840 Ω ∴ Resistance of 1 bulb = 4840Ω For a flow of 5A current, we need to find the equivalent resistance of the circuit. ∴ Req =\(\frac{V}{l}\) = \(\frac{220}{5}\) = 44Ω In parallel combination, \(\frac{1}{R_{eq}}\) = \(\frac{1}{R}\) + \(\frac{1}{R}\) + \(\frac{1}{R}\) +............... (n times) Or, \(\frac{1}{R_{eq}}\) = n x \(\frac{1}{R}\) ∴ n = \(\frac{R}{R_{eq}}\) = \(\frac{4840}{44}\) = 110 ∴ 110 lamps have to be connected in parallel. |
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