Question 457: Electrostatics & Capacitance

Question

Two parallel plate air c apacitors of same capacity ' C ' are connected in parallel to a battery of e.m.f. ' $E$ '. Then one of the capacitors is completely filled with dielectric mnaterial of constant ' K '. The change in the effective capacity of the parallel combination is

Accepted Answer

Let the capacitance of each air capacitor be $C$.
Step 1: Initial effective capacitance (before inserting dielectric)
Since both capacitors are identical and connected in parallel:
$$ C_{	ext{initial}} = C + C = 2C $$
Step 2: Insert dielectric of constant $K$ in one capacitor
The capacitance of the capacitor with dielectric becomes:
$$ C' = K C $$
So the effective capacitance of the parallel combination is:
$$ C_{	ext{final}} = C + K C = (1+K)C $$
Step 3: Change in effective capacitance
Change in effective capacitance is:
$$ \Delta C = C_{	ext{final}} - C_{	ext{initial}} $$
Substitute the values:
$ \Delta C = (1+K)C - 2C = (K - 1)C $
Step 4: Match with the options
So, the correct answer is
$ \boxed{\mathrm{C}(\mathrm{K}-1)} $
Option D is correct.

Answer

$\frac{\mathrm{C}}{(\mathrm{K}-1)}$

Answer

$\frac{\mathrm{KC}}{\mathrm{K}-1}$

Answer

$\mathrm{KC}+1$

Answer

$\mathrm{C}(\mathrm{K}-1)$

Electrostatics & Capacitance

Two parallel plate air c apacitors of same capacity ' C ' are connected in parallel to a battery of e.m.f. ' E '. Then one of the capacitors is completely filled with dielectric mnaterial of constant ' K '. The change in the effective capacity of the parallel combination is

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