3(a) This means that the ratio of the charge on the capacitor to the potential difference between the plates is 4LF.
(b)(i) (1) Area of plates
(2) Dielectric between plates
(3) Distance between plates
(b)(ii) (1) To separate a.c from d.c.
(2) To control current in a.c circuit
(3) To store charges or energy
(c) Workdone, W = QV
Average work done is given by \(\frac{1}{2}\) x QV .........(i)
But V = \(\frac{Q}{V}\) ...............(ii)
Substituting (ii) in (i)
W = \(\frac{1}{2}\) x Q x \(\frac{Q}{C}\)
Energy stored W = \(\frac{1}{2} \times \frac{Q^2}{2} \frac{1}{2} \frac{Q^2}{C}\)
(i) Q\(_2 = C_2V\)
= 100 x 10\(^{-6}\) C = 100\(mu\)C
\(Q_1 = C_1 V\)
= 3 10\(^{-6}\) x 50 = 150\(\mu\)C
(iii) P.d across each capacitor is 50V
(iii) E = \(\frac{1}{2} CV^2\) Since capacitors are in parallel
C = \(\frac{1}{2}\) x 5 \(\mu\)F x 50 x 50
= \(\frac{1}{2}\) x 5 x 10\(^{-6}\) x 50 x 50 = 6.25 x 10\(^{-3}\)J