Two parallel plate capacitor of capacitances C and 2C are connected in parallel and charged to a potential difference V . If the battery
is disconnected and the space between the plate of the capacitor of capacince C is completely filled with a material of dielectric constant K, then the potential difference across the capacitor will be come

Question

Verified by Toppr

Answer 1

The original capacitance of the parallel combination of C and 2 C is = C +2C = 3C

Total charge Q = 3CV

When the capacitor C is filled with a dielectric, its capacitance becomes KC.

Therefore, after the capacitor is filled with dielectric the capacitance of the combination, C' = KC + 2C = C (K + 2).

However, the charge remains the same, i.e. Q = 3CV

Therefore, the potential difference across the capacitors will be

$begin mathsize 12px style fraction numerator Q over denominator C apostrophe end fraction equals fraction numerator 3 C V over denominator open parentheses K space plus space 2 close parentheses begin display style C end style end fraction therefore fraction numerator begin display style Q end style over denominator begin display style C apostrophe end style end fraction equals fraction numerator begin display style 3 V end style over denominator begin display style open parentheses K space plus space 2 close parentheses end style end fraction end style$

Answer 2

The original capacitance of the parallel combination of C and 2 C is = C +2C = 3C

Total charge Q = 3CV

When the capacitor C is filled with a dielectric, its capacitance becomes KC.

Therefore, after the capacitor is filled with dielectric the capacitance of the combination, C' = KC + 2C = C (K + 2).

However, the charge remains the same, i.e. Q = 3CV

Therefore, the potential difference across the capacitors will be

$begin mathsize 12px style fraction numerator Q over denominator C apostrophe end fraction equals fraction numerator 3 C V over denominator open parentheses K space plus space 2 close parentheses begin display style C end style end fraction therefore fraction numerator begin display style Q end style over denominator begin display style C apostrophe end style end fraction equals fraction numerator begin display style 3 V end style over denominator begin display style open parentheses K space plus space 2 close parentheses end style end fraction end style$

$3 V (K + 2)$

$\frac{( K + 2 )}{3 V}$

$\frac{3 V}{( K + 2 )}$

$\frac{3 ( K + 2 )}{V}$

The energy per unit volume of a dielectric medium is proportional to square of

A parallel plate capacitor of capacitance $6 μ F$ in air and $60 μ F$ . When dielectric is introduced. What is the dielectric constant of the medium.?

If the dielectric constant of a substance is $K = \frac{4}{3}$ , then the electric susceptibility $Ψ_{e}$ is:

Water is not used as a dielectric between the plates of a capacitor because its.

If the susceptibility of dia, para and ferro magnetic materials are $X d . X p . X f$ respectively, then

Revise with Concepts

Dielectrics-Polar and Non-polar Dielectric Molecules

Basic Knowledge of Polarisation of Dielectrics

3V(K+2)

3V(K+2)​

(K+2)3V​

V3(K+2)​