Two heating elements of resistances $R_{1}$ and $R_{2}$ when operated at a constant supply of voltage, $V$, Consume power $P_1$ and $P_2$ respectively. Deduce the expressions for the power of their combination when they are, in turn, connected in $(i)$ series and $(ii)$ parallel across the same voltage supply.
CBSE OUTSIDE DELHI - SET 1 2011
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$P_1=\frac{V^2}{R_1}$
$P_2=\frac{V^2}{R_2}$
In Series
$P=\frac{V^2}{{R_1}+{R_2}}$
Alternatively
$p=\frac{V^2}{V^2\bigg(\frac{1}{p_1}+\frac{1}{p_2}\bigg)}$
$\frac{1}{p }=\frac{1}{p_1 }+\frac{1}{p_2 }$
In Parallel
$P=\frac{V^2(R_1+R_2)}{R_1+R_2}$
Alternatively
$P=\frac{V^2}{R}=\frac{V^2(P_1+P_2)}{V^2}$
$P=P_1+P_2 $
$P_2=\frac{V^2}{R_2}$
In Series
$P=\frac{V^2}{{R_1}+{R_2}}$
Alternatively
$p=\frac{V^2}{V^2\bigg(\frac{1}{p_1}+\frac{1}{p_2}\bigg)}$
$\frac{1}{p }=\frac{1}{p_1 }+\frac{1}{p_2 }$
In Parallel
$P=\frac{V^2(R_1+R_2)}{R_1+R_2}$
Alternatively
$P=\frac{V^2}{R}=\frac{V^2(P_1+P_2)}{V^2}$
$P=P_1+P_2 $
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