A parallel plate capacitor of plate area A an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Since the battery is disconnected,the charge $Q$ on the plates remains constant.Initial charge $Q = C V = \frac{\varepsilon_0 A}{d} V$.When a diel

Vedclass · Accepted Answer

all of the above

Vedclass · Answer

(D) Since the battery is disconnected,the charge $Q$ on the plates remains constant.Initial charge $Q = C V = \frac{\varepsilon_0 A}{d} V$.When a dielectric slab of constant $K$ is inserted,the new capacitance becomes $C' = KC = \frac{K\varepsilon_0 A}{d}$.The new potential difference is $V' = \frac{Q}{C'} = \frac{Q}{KC} = \frac{V}{K}$.The new electric field is $E = \frac{V'}{d} = \frac{V}{Kd}$.The initial potential energy is $U_i = \frac{1}{2}CV^2 = \frac{\varepsilon_0 AV^2}{2d}$.The final potential energy is $U_f = \frac{1}{2}C'V'^2 = \frac{1}{2}(KC) \left(\frac{V}{K}\right)^2 = \frac{1}{2} \frac{CV^2}{K} = \frac{\varepsilon_0 AV^2}{2Kd}$.The work done on the system is $W = U_f - U_i = \frac{\varepsilon_0 AV^2}{2Kd} - \frac{\varepsilon_0 AV^2}{2d} = -\frac{\varepsilon_0 AV^2}{2d} \left(1 - \frac{1}{K}\right)$.

Similar Questions

The variation of the electric field between the plates of a capacitor is shown in the figure. Find the relation between $K_1$,$K_2$,and $K_3$,if $2x = y$.

$A$ parallel plate capacitor is charged to a potential of $100 \ V$. $A$ dielectric slab of thickness $2 \ mm$ is inserted between the plates. To maintain the same potential difference,the distance between the plates is increased by $1.6 \ mm$. The dielectric constant of the slab is:

Explain the effect of a dielectric on the capacitance of a parallel plate capacitor and obtain the formula for the dielectric constant.

$A$ capacitor, when filled with a dielectric $K = 3$, has charge $Q_0$, voltage $V_0$, and electric field $E_0$. If the dielectric is replaced with another one having $K = 9$, the new values of charge, voltage, and field will be respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module