Examples for capacitors

Example #1


Consider two plates separated by d=1.5 cm , where the electric field between them is 100 V/m, and the charge on the plates is 30.0 mC. What is the capacitance?


The Capacitance is:

2.0E-5 F

Example #2


Consider a capacitor made of two 0.05 m2 plates separated by 0.5 mm. If the capacitance is 3.0 nf, what is the relative permeability, k, of the material between the plates?



Example #3

Problem: part a.)

What is the capacitance of the following segment of a circuit?

DATA: C1=C2=C3=3.0 mf


The capacitance of the two in parallel is C23=C2+C3. The capacitance of the entire circuit is:

*** change C_34 to C_23 ***

2.0 (mF)

part b.)

If a voltage Vab = 6.0 V is applied, what is the charge on each capacitor?


The charge on the first capacitor is the same as the charge on the whole combination, since it is the only thing the left-hand wire is connected to. This charge can be found from the capacitance.

There is a charge Q1 on the opposite side of the first capacitor, which must have come equally from the next capacitors since they are equal to each other. Therefore, Q2=Q3=(1/2)Q1.

Q1 = 12 mC,     Q2 = Q3 = 6.0 mC

part c.)

What is the voltage across each capacitor?


Use Vi=Qi/Ci. Check when you are done that the voltages add up to 6.0 V.

V1 = 4.0 V,     V2 = V3 = 2.0 V

Example #4


A capacitor has a charge of 3.0 nC when the voltage across the capacitor is 12 V. What is the energy stored in the capacitor?


The energy is:

18 E-9 J

Capacitors index        Lecture index