Two identical parallel plate air capacitors are connected in series to a battery of emf V . If one of the capacitor is completely filled with dielectric material of constant K , then potential differe

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Two identical parallel plate air capacitors are connected in series to a battery of emf V . If one of the capacitor is completely filled with dielectric material of constant K , then potential difference of the other capacitor will become

TestHub · Accepted Answer

Both the capacitance will have same charge $V_{1} = \frac{q}{C}$ and $V_{2} = \frac{q}{K C}$
But $V_{1} + V_{2} = V$
$\Rightarrow \frac{q}{C} + \frac{q}{K C} = V$
$\Rightarrow \frac{q}{C} . \frac{K + 1}{K} = V$
Potential difference across capacitor without dielectric is
$V' = \frac{q}{C} = \frac{K}{K + 1} V$

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