Question

Instructions: Show the whole solutions in each question.

1. Determine the net capacitance of the capacitor combination when the capacitances are C1=12µF, C2=2µF, C3=4µF When the 12V potential difference is maintained across the combination, find the charge and the voltage across each capacitor.

2. Compute the capacitance of a capacitor with two parallel plates and separated by a layer of paraffin that is 0.25cm thick. The area of each plate is 70cm^2, and the dielectric constant of paraffin is 2.

Answer 1

1. The net capacitance

$$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$$

$$\frac{1}{C}=\frac{1}{12\:\rm \mu F}+\frac{1}{2\:\rm \mu F}+\frac{1}{4\:\rm \mu F}$$

$$C=1.2\:\rm \mu F$$

The charge at the plates of capacitors

$$q_1=q_2=q_3=CV\\ =1.2*10^{-6}*12=14.4\:\rm \mu C$$

The voltage

$$V_1=q_1/C_1=14.4/12=1.2\:\rm V$$

$$V_2=q_2/C_2=14.4/2=7.2\:\rm V$$

$$V_3=q_3/C_3=14.4/4=3.6\:\rm V$$

2. The capacitance of a parallel plate capacitor

$$C=\frac{\kappa\epsilon_0A}{d}\\ =\frac{2*8.85*10^{-12}*70*10^{-4}}{0.25*10^{-2}}=50*10^{-12}\:\rm F=50\: pF$$