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 ?
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 ?
solution:
Resistance of each bulb, $R=\frac{V^{2}}{P}=\frac{(220)^{2}}{10}=4840 \Omega$
Total resistance in the circuit, $\mathrm{R}_{*}=\frac{220}{5}=44 \Omega$
Let $\mathrm{n}$ be the number of bulb (each of resistance $\mathrm{R}$ ) to be connected in parallel to obtain a resistance $\mathrm{R}_{\mathrm{e}}$.
Clearly, $\quad \mathrm{R}_{\mathrm{e}}=\frac{\mathrm{R}}{\mathrm{n}}$ or $\mathrm{n}=\frac{\mathrm{R}}{\mathrm{R}_{\mathrm{e}}}=\frac{4840}{44}=\mathbf{1 1 0}$
Resistance of each bulb, $R=\frac{V^{2}}{P}=\frac{(220)^{2}}{10}=4840 \Omega$
Total resistance in the circuit, $\mathrm{R}_{*}=\frac{220}{5}=44 \Omega$
Let $\mathrm{n}$ be the number of bulb (each of resistance $\mathrm{R}$ ) to be connected in parallel to obtain a resistance $\mathrm{R}_{\mathrm{e}}$.
Clearly, $\quad \mathrm{R}_{\mathrm{e}}=\frac{\mathrm{R}}{\mathrm{n}}$ or $\mathrm{n}=\frac{\mathrm{R}}{\mathrm{R}_{\mathrm{e}}}=\frac{4840}{44}=\mathbf{1 1 0}$
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