Question

When the top right-hand capacitor is filled with a material of dielectric constant κ, the charge on this capacitor is increases by a factor of 1.35. Find the dielectric constant κ of the material inserted into the top right-hand capacitor.

Answer 1

Answer: k = 2.07692

Explanation: Please find the attached files for the solution

Answer 2

Answer:

Explanation:

Given:

Capacitance, c1 = c2 = c3 = c4

= 80 micro farad

Voltage, v = Eb

= 4 V

We are not concerned with c3 and c4 just c1 and c2,

Since c1 and c2 are in series,

1/ct = 1/c1 + 1/c2

vab = v1 + v2

= q'/c1 + q'/c2

But c2 = κ × c,

= q'/c + q'/κc  .....1

Let c1 = c2 = c,

Vab = q/c + q/c

= 2 × q/c. ........2

Equating equation 1 and 2,

q'/c + q'/κc = 2q/c

q'/c × (1 + 1/κ) = 2q/c

q'/q = 2κ/(1 + κ)

But q'/q = 1.35

2κ/(1 + κ) = 1.35

0.65κ = 1.35

κ = 1.35/0.65

= 2.077