Home
Class 12
PHYSICS
A capacitor is filled with two dielectr...

A capacitor is filled with two dielectrics of same dimensions, but of dielectric constants 2 and 3 respectively. Find the ratio of capacitances in the two arrangements shown in Fig.

Text Solution

Verified by Experts

As is clear from Fig.
`C_(1) = (in_(0) AK_(1))/(d//2) , C_(2) = (in_(0) AK_(2))/(d//2)`
These capacitors are joined in series, therefore equivalent capacity
`C = (C_(1) C_(2))/(C_(1) + C_(2)) = (((2 in_(0) K_(1)A)/(d)) ((2 in_(0) K_(2) A)/(d)))/((2in A)/(d) (K_(1) + K_(2)))`
`C = (2 in_(0) A K_(1) K_(2))/(d (K_(1) + K_(2)))` ...(i)
in Fig.
`C_(3) = (in_(0) K_(1) (A//2))/(d) , C_(4) = (in_(0) K_(2) (A//2))/(d)`
These capacitors are joined in parallel, therefore equivalent capacity
`C' = C_(3) + C_(4) = (in_(0) A)/(2d) (K_(1) + K_(2))` ....(ii)
Now, `(C )/(C') = (2in_(0) A K_(1) K_(2))/(d (K_(1) + K_(2))) xx (2d)/(in_(0) A (K_(1) + K_(2)))`
`= (4 K_(1) K_(2))/((K_(1) + K_(2))^(2)) = (4xx2xx3)/((2+3)^(2) )= (24)/(25)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The capacitance of a capacitor, filled with two dielectrics of same dimensions but of dielectric constants K_1 and K_2 respectively as shown will be -

The space between parallel plate capacitors is filled with four dielectrics of equal dimensions but of dielectric constants K_(1), K_(2), K_(3)andK_(4) respectively. If K is the dielectric constant of a single dielectric that must be filled between capacitor plates to have the same capacitance between A and B. Then we must have

Capacitor has square plates of side l .Three dielectrics fill the space as shown (their dielectric constants are given).Find equivalent capacitance.

The figure shows two identical parallel plate capacitors connected to a battery with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant(or relative permittivity) 3. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.

The capacitance of a parallel plate capacitor with plate area A and separation d is C . The space between the plates in filled with two wedges of dielectric constants K_(1) and K_(2) respectively. Find the capacitance of resulting capacitor.

A parallel plate capacitor of plate area A and separation d is filled with two materials each of thickness d/2 and dielectric constants in_1 and in_2 respectively. The equivalent capacitance will be