A parallel plate capacitor is filled by a di-electric whose relative permittively varies with the applied voltage according to the law `=alpha V`, where `alpha = 1` per volt. The same (but contiaining no di-electirc) capacitor charged to a voltage `V = 156` volt is connected in parallel to the first ''non-linear'' uncharged capacitor. Determine the final voltage `V_(f)` across the capacitors.

Options

A. 6V
B. 12V
C. 8V
D. 4V

Answer

B

Explanation

The capacitance of the nonlinear capacitor is
`C=epsilonC_(0)=alpha VC_(0)`
where `C_(0)` is the capacitance of the capacitor without a dielectric. The charge on the nonlinear capacitor is `q_(n)=CV=alphaC_(0)V^(2)`, where the charge on the normal capacitor is `q_(0)=C_(0)V`. it follows from the charge conservation law `q_(n)+q_(0)=C_(0)V_(0)`
that the required voltage is `V=(sqrt(4alphaV_(0)+1)-1)/(2alpha)=12V`