Partially Filled Dielectrics

Q. Find the ceff for this system having a variable dielectric

1. $\frac{k{ϵ}_{0}A}{ln\left(3\right)d}$
2. $\frac{k{ϵ}_{0}A}{ln\left(2\right)d}$
3. $\frac{3k{ϵ}_{0}A}{2d}$
4. $\frac{k{ϵ}_{0}A}{2d}$

Q.

Find the effective capacitance of the following system.

1. $\frac{(k_1+k_2){ϵ}_{0}A}{d}$
2. $\frac{{ϵ}_{0}A{k}_1{k}_2}{(k_1+k_2)d}$
3. $\frac{{ϵ}_0{k}_1{k}_{2}A}{(k_1-k_2)d}ln\left(\frac{k_1}{k_2}\right)$
4. $\frac{{ϵ}_0(k_1+k_2)A}{d}ln\left(\frac{k_1}{k_2}\right)$

Q. Find $C_{eff}$

1. $\frac{{ϵ}_{0}A}{d-t_1-t_2+t_1/k+t_2/k}$
2. $\frac{{ϵ}_{0}A}{d-t_1-t_2-t_1/k-t_2/k}$
3. $\frac{{ϵ}_{0}A}{d+t_1+t_2+t_1/k+t_2/k}$
4. $\frac{{ϵ}_{0}A}{d+t_1+t_2-t_1/k-t_2/k}$

Q. Find Ceff

1. $\frac{{ϵ}_{0}A}{d}(k_1+k_2)$
2. $\frac{{ϵ}_{0}A}{2d}(k_1+k_2)$
3. $\frac{{ϵ}_{0}A}{d}\left(\frac{k_1{k}_2}{k_1+k_2}\right)$
4. None of these

Q. Find the effective capacitance of the following system. Having a variable dielectric

1. $\frac{k{ϵ}_{0}A}{2d}$
2. $\frac{k{ϵ}_{0}A}{d}$
3. $\frac{2k{ϵ}_{0}A}{3d}$
4. $\frac{3k{ϵ}_{0}A}{2d}$

Q. Find Ceff

1. $\frac{{ϵ}_{0}A}{2d}\left(\frac{k_1{k}_2{k}_3}{k_1{k}_3+k_2{k}_3}\right)$
2. $\frac{{ϵ}_{0}A}{d}(k_1+k_2+k_3)$
3. $\frac{{ϵ}_{0}A}{2d}(k_3+\frac{2k_1{k}_2}{k_1+k_2})$
4. $\frac{{ϵ}_{0}A}{d}(k_3+\frac{2k_1{k}_2}{k_1+k_2})$

Q. Find Ceff

1. $\frac{17k{ϵ}_{0}A}{12d}$
2. $\frac{2k{ϵ}_{0}A}{4d}$
3. $\frac{5k{ϵ}_{0}A}{3d}$
4. $\frac{k{ϵ}_{0}A}{4d}$

Q. Find ceff

1. $\frac{k{ϵ}_{0}A}{d}$
2. $\frac{{ϵ}_{0}A}{d}\left(\frac{k+1}{k}\right)$
3. $\frac{{ϵ}_{0}A}{d}\left(\frac{2k+1}{k+1}\right)$
4. $\frac{{ϵ}_{0}A}{2d}\left(\frac{3k+1}{k+1}\right)$

Q. After inserting a dielectric inside a parallel plate capacitor, charge on the plates .

1. increases
2. decreases
3. remains same

Q. A parallel-plate capacitor has a dielectric slab in it. The slab just fills the space inside the capacitor. The capacitor is charged by a battery and then the battery is disconnected. Now, the slab is pulled out slowly at $t=0$. If at time $t$, the capacitance of the capacitor is $C$ and potential difference between the plates of the capacitor is $V$, then which of the following graphs is/are correct.

1. 
2. 
3. 
4.