Two air capacitors A = 1 μ F; B = 4 μ F are connected in series with 35 V source. When a medium of dielectric constant K = 3 is introduced in between the plates of A, charge on the capacitors changes by

Question

Two air capacitors A = 1 μ F; B = 4 μ F are connected in series with 35 V source. When a medium of dielectric constant K = 3 is introduced in between the plates of A, charge on the capacitors changes by (A)  32 μ C  (B)  16 μ C  (C)  60 μ C  (D)  28 μ C

Tardigrade Admin · Accepted Answer

Initial situation is shown in the figure .
Net capacitance,

C = \frac{A B}{A + B} = \frac{4}{5} μ F

Charge through the circuit,

Q = C V

= \frac{4}{5} \times 1 0^{- 6} \times 35 = 28 μ C

When dielectric of dielectric constant

K = 3

is introduced in between the plates of

A

So its capacitance,

A^{'} = K A = 3 μ F

Now,

A^{'}

and

B

are in series, so net capacitance of the circuit,

C^{'} = \frac{A ^{'} B}{A ^{'} + B} = \frac{3 \times 4}{3 + 4} = \frac{12}{7} μ F

Charge through the circuit

Q^{'} = C^{'} V = \frac{12}{7} \times 1 0^{- 6} \times 35 = 60 μ C

Change in the charge on the capacitors

= Q^{'} - Q = 60 - 28 = 32 μ C .

Q. Two air capacitors $A = 1 μ F; B = 4 μ F$ are connected in series with $35 V$ source. When a medium of dielectric constant $K = 3$ is introduced in between the plates of $A$ , charge on the capacitors changes by

$32 μ C$

$16 μ C$

$60 μ C$

$28 μ C$

Q. Two air capacitors A=1μF;B=4μF are connected in series with 35V source. When a medium of dielectric constant K=3 is introduced in between the plates of A, charge on the capacitors changes by

32μC

16μC

60μC

28μC

Q. Two air capacitors $A = 1 μ F; B = 4 μ F$ are connected in series with $35 V$ source. When a medium of dielectric constant $K = 3$ is introduced in between the plates of $A$ , charge on the capacitors changes by

$32 μ C$

$16 μ C$

$60 μ C$

$28 μ C$