There is a closed system that contains 2 circuits parallel to each other. Each c

Question

There is a closed system that contains 2 circuits parallel to each other. Each circuit has right and left capacitors, resulting in a total of 4. The upper circuit is parallel to the lower circuit. Each capacitor has a capacitance of 57.4 uF. The battery provides 70.1V. When the top right-hand capacitor is filled with a material of dielectric constant k, the charge on this capacitor is increases by a factor of 1.43. Find the dielectric constant k of the material inserted into the top right-hand capacitor.

I thought the answer is simply k=1.43... but apparently it's wrong. Help?

Explanation / Answer

Cnet = C/2 uF

Q = Cnet*V = CV/2 uC

---------
C'net = (C*k*C)/(C+k*C)

C' = kC/(K+1)

Q' = C'*V = k*C*V/(K+1)

Q'/Q = 1.43

k*2/(K+1) = 1.43

2k = 1.43k + 1.43

0.57k = 1.43

k = 2.51

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