Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V?
Given: P1 = 100 W, P2 = 60 W and 7 = 220 V
Resistance of first lamp,
R1 = \(\frac{V^2}{P_1}\) = \(\frac{220 \times 220}{100}\)
= 484Ω
Resistance of second lamp,
R2 = \(\frac{V^2}{P_2}\) = \(\frac{220 \times 220}{60}\)
= \(\frac{2420}{3}\)Ω
Let Rp be the equivalent resistance. Then
\(\frac{1}{R_p}\) = \(\frac{1}{R_1}\) + \(\frac{1}{R_2}\) [∴ Lamps are in series]
= \(\frac{1}{484}\) + \(\frac{1}{\frac{2420}{3}}\)
= \(\frac{1}{484}\) + \(\frac{3}{2420}\)
= \(\frac{5+3}{2420}\) = \(\frac{8}{2420}\)
∴ Rp = \(\frac{2420}{8}\)Ω
Now applying the formula V = IR, We get
I = \(\frac{V}{R}\) = \(\frac{220}{\frac{2420}{8}}\)
= \(\frac{220 \times 8}{2420}\) = 0.73A [∵ R = Rp]
Hence, 0.73 A current is drawn from the line.