Question

1. Download the University of Colorado Boulder Physics Education Technology (PhET) capacitor-lab java applet from Blackboard, found in the “Lab” tab under the “Lab 2 - Capacitance” heading.

Capacitance

2. To increase the total charge stored on two capacitors should you connect them to a battery in series or in parallel? Why? Explain your answer and verify with the PhET simulation.

3. To increase the potential drop across two capacitors should you connect them in series or in parallel? Why? Explain your answer.

Capacitors with a Dielectric

4. Derive an expression for the total charge Qtotal on two parallel-plate capacitors connected in parallel to a battery providing a potential V, both with the same area A and separation d, and one filled with an insulator of dielectric constant κ. Simplify the expression as much as possible. Your expression should be in terms of V, A, d,κ, and ε0.

5. Using the PhET simulation on the Dielectric tab, create a capacitor of plate area A = 400 mm2 and separation d = 8.0 mm, and slide a glass dielectric so that it fills half of the volume between the plates. Set the battery to provide a potential of approximately 1.20 V. What is the charge Q on the capacitor?

6. Use your previously derived equation for the total charge on capacitors in parallel to calculate the total charge on two capacitors in parallel with the quantities given above. How does it compare to what you found in the simulation? What does this lead you to conclude?

Multiple Capacitors

7.Determine the total charge Qtotal in a circuit with a battery providing a potential of V = 1.26 V and three capacitors with capacitances C1 = 0.27 pF, C2 = 0.19 pF, and C3= 0.15 pF (pF = 10-12 F) connected in the following manner:

(a) C1, C2, and C3 all in series
(b) C1, C2, and C3 all in parallel
(c) C1 and C2 in series, and C12 in parallel with C3(d) C2 and C3 in parallel, and C23 in series with C1

8:Verify the previous calculations by constructing the circuits in the PhET simulation, and in each case (a)-(d) measure and record the voltage drops across each of the capacitors.

Answer 1

a)We know when capacitors are connected in series the charge through each capacitor is same.

Q=CV

b) Equal capacitance when all connected in parallel

Ceq=C1+C2+C3=0.27pF+0.19pF+0.15pF=0.61pF

Q=CV=0.61*10^{-12}*1.26= 0.7686pC

c)When C1 AND C2 are in series

C12=0.112*10^{-12} F

Ceq=C12+C3       {in parallel}

Ceq=0.112*10^{-12} F +0.15*10^{-12} F=0.262*10^{-12} F

Q=CV=0.262*10^{-12} * 1.26=0.33*10^{-12} C

d)When C2 AND C3 are in parallel

C23=C2+C3=(0.19+0.15) pF=0.34pF

C23 in series with c1

Ceq=1.51*10^{-13} F

Q=CV=1.51*10^{-13}*1.26=1.9*10^{-13} C