Question

If the above capacitor is connected across a 6⋅0 V battery, find (a) the charge supplied by the battery, (b) the induced charge on the dielectric and (c) the net charge appearing on one of the coated surfaces.

Answer 1

a) The charge supplied by the battery = 8.5 nC

b) Induced charge on the dielectric = 6.4 nC

c) Charge appearing on one of the coated surfaces = 2.1 nC

Explanation:

Given:

Capacitance of the capacitor, $C=1.42 \mathrm{nF}$

Dielectric constant, k = 4

Voltage of the battery connected, V = 6 V

(a) The charge supplied by the battery is given by

$q=C V$

  $=1.42 \times 10^{-9} \times 6$

  $=8.52 \times 10^{-9} \mathrm{C}$

  $=8.5 \mathrm{nC}$

(b) The charge induced on the dielectric is given by

$q^{\prime}=q\left(1-\frac{1}{K}\right)$

   $=8.52 \times 10^{-9} \times(1-0.25)$

   $=6.39 \times 10^{-9}=6.4 \mathrm{nC}$

(c) The charge appearing on one of the coated plates is given by

$Q_{\text {net }}=8.5-6.4=2.1 \mathrm{nC}$