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