Two lamps, one rated 100 W at 220 V

Question.
Two lamps, one rated $100 \mathrm{~W}$ at $220 \mathrm{~V}$, and the other $60 \mathrm{~W}$ at $220 \mathrm{~V}$, are connected in parallel to the electric mains supply. What current is drawn from the line if the supply voltage is 220 V ?

solution:
Resistance of first lamp,

$R_{1}=\frac{V^{2}}{P}=\frac{(220)^{2}}{100}$

resistance of the second lamp,

$\mathrm{R}_{2}=\frac{\mathrm{V}^{2}}{\mathrm{P}}=\frac{(220)^{2}}{60}$

Since the two lamps are connected in parallel, the equivalent resistance is given by

$\frac{1}{\mathrm{R}_{\mathrm{p}}}=\frac{1}{\mathrm{R}_{1}}+\frac{1}{\mathrm{R}_{2}}=\frac{100}{(220)^{2}}+\frac{60}{(220)^{2}}=\frac{160}{(220)^{2}}$

or $\mathrm{R}_{\mathrm{P}}=\frac{(220)^{2}}{160}=\mathbf{3 0 2 . 5} \boldsymbol{\Omega}$

Current drawn from the line, i.e.,

$I=\frac{V}{R_{p}}=\frac{220 V}{302.5 \Omega}=0.727 \mathrm{~A}$

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