The parallel combination of two air filled parallel plate capacitors of capacitance C and n C is connected to a battery of voltage, V . When the capacitors are fully charged, the battery is removed an

Question

The parallel combination of two air filled parallel plate capacitors of capacitance C and n C is connected to a battery of voltage, V . When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed the two plates of the first capacitor. The new potential difference of the combined system is:

TestHub · Accepted Answer

i)

ii) Battery disconnected after full charge,
Total charge of the system,
$= C V + n C V$
$= (n + 1) C V$

iii) Inserting dielectric of constant $K$

Common potential, $V_{C} = \frac{t o t a l c h a r g e}{t o t a l c a p a c i t a n c e}$
$= \frac{(n + 1) C V}{K C + n C} = \frac{(n + 1) V}{K + n}$

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