Two capacitors of capacitance C are connected in series. If one of them is filled with dielectric substance K, what is the effective capacitance?

Question

Two capacitors of capacitance C are connected in series. If one of them is filled with dielectric substance K, what is the effective capacitance? (A)  (KC/(1+K))  (B) C (K + 1) (C)  (2KC/K+1)  (D) None of these

Tardigrade Admin · Accepted Answer

When plates of capacitor are separated by a dielectric medium of dielectric constant

K

,
its

C_{m} = \frac{K ε _{0} A}{d} = K C_{0}

i e,

C_{m} = K C_{0}

Here,

C_{0} = C

∴

C_{m} = K C

Now, two capacitors of capacities

K C

and

C

are in series, their effective capacitance

\frac{1}{C} = \frac{1}{K C} + \frac{1}{C}

or

\frac{1}{C} = \frac{1 + K}{K C}

∴

C = \frac{K C}{K + 1}

Q. Two capacitors of capacitance C are connected in series. If one of them is filled with dielectric substance K, what is the effective capacitance?

$\frac{K C}{( 1 + K )}$

C (K + 1)

$\frac{2 K C}{K + 1}$

None of these

Q. Two capacitors of capacitance C are connected in series. If one of them is filled with dielectric substance K, what is the effective capacitance?

(1+K)KC​

C (K + 1)

K+12KC​

None of these

$\frac{K C}{( 1 + K )}$

$\frac{2 K C}{K + 1}$