A heater $A$ gives out $300\, W$ of heat when connected to a $200\, V$ $d.c.$ supply. Asecond heater $B$ gives out $600\, W$ when connected to a $200\,v$ $d.c$. supply. If a series combination of the two heaters is connected to a $200\, V$ $d.c$. supply the heat output will be ................. $W$
Diffcult
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The two heaters with different power are connected in series,
$P 1=\frac{V^{2}}{R 1}$ and $P 2=\frac{V^{2}}{R 2}$
therefore,
$R 1=\frac{V^{2}}{P 1}$ and $R 2=\frac{V^{2}}{P 2}$
in series combination
$R_{e q}=R 1+R 2$
Hence,
$P_{e q}=\frac{V^{2}}{P 1}+\frac{V^{2}}{P 2}$
$P_{e q}=\left(\frac{1}{2}\right) V^{2}$
$P_{e q}=\frac{1}{2}(400)=200 W$
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