Two exactly similar electric lamps are arranged (i) in parallel, and (ii) in series. If the parallel and series combination of lamps are connected to 220V supply line one by one, what will be the ratio of electric power consumed by them?
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Let resistance of each lamp = R ohms.
Case1: Parellel connection
Resultant resistance $=\frac{1}{\frac{1}{\text{R}}+\frac{1}{\text{R}}}=\frac{\text{R}}{2}$
Electric power consumed $\text{P}_1=\frac{\text{V}_2}{\text{R}}=\frac{220^2}{\frac{\text{R}}{2}}=\frac{96800}{\text{R}}$
Case2: Series connection
Resultant resistance = R + R = 2R
Electric Power consumed $\text{P}_2=\frac{\text{V}^2}{2\text{R}}=\frac{24200}{\text{R}}$
$\therefore\frac{\text{P}_1}{\text{P}_2}=\frac{\frac{96800}{\text{R}}}{\frac{24200}{\text{R}}}=\frac{4}{1}$
Case1: Parellel connection
Resultant resistance $=\frac{1}{\frac{1}{\text{R}}+\frac{1}{\text{R}}}=\frac{\text{R}}{2}$
Electric power consumed $\text{P}_1=\frac{\text{V}_2}{\text{R}}=\frac{220^2}{\frac{\text{R}}{2}}=\frac{96800}{\text{R}}$
Case2: Series connection
Resultant resistance = R + R = 2R
Electric Power consumed $\text{P}_2=\frac{\text{V}^2}{2\text{R}}=\frac{24200}{\text{R}}$
$\therefore\frac{\text{P}_1}{\text{P}_2}=\frac{\frac{96800}{\text{R}}}{\frac{24200}{\text{R}}}=\frac{4}{1}$
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