CBSE 2024 · Region 4 · Set 1 · Q20 · 2 marks
Two electric heaters have power ratings $\displaystyle \mathrm{P}_{1}$ and $\displaystyle \mathrm{P}_{2}$, at voltage V . They are connected in series to a dc source of voltage V. Find the power consumed by the combination. Will they consume the same power if connected in parallel across the same source ?
Marking-scheme solution
$\displaystyle R_{1}=\frac{V^{2}}{P_{1}}$ & $\displaystyle R_{2}=\frac{V^{2}}{P_{2}}$
$\displaystyle R_{e q}=R_{1}+R_{2}=V^{2}\left(\frac{1}{P_{1}}+\frac{1}{P_{2}}\right)$
$\displaystyle P_{\text {series }}=\frac{V^{2}}{R_{e q}}$
$\displaystyle P_{\text {series }}=\frac{V^{2}}{V^{2}\left(\dfrac{1}{P_{1}}+\dfrac{1}{P_{2}}\right)}$
$\displaystyle \frac{1}{P_{\text {series }}}=\frac{1}{P_{1}}+\frac{1}{P_{2}}$
No.
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