1. Physics 102: Lecture 4, Slide 1
SPH4UW
Capacitors!
Physics 102: Lecture 4, Slide 1

2. Capacitance: The ability to store separated charge C=Q/V
Charge Q on plates
Charge 2Q on plates
V = VA – VB = +E0 d
V = VA – VB =+2E0d
E=2E0
E=E0 + - + - + - A B A B
Use fire extinguisher analogy? d d
Potential difference is proportional to charge: Double Q  Double V
Q = CV

3. Capacitor
Any pair conductors separated by a small distance. (e.g. two metal plates)
Capacitor stores separated charge
Positive Q on one conductor, negative Q on other
Net charge is zero
Q=CV E d + -
Stores Energy
U =(½) Q V

4. Capacitance Practice
How much charge is on a 0.9 F capacitor which has a potential difference of 200 Volts?
Q = CV
= (0.9)(200) = 180 Coulombs
How much energy is stored in this capacitor?
U = ½ Q V
= ½ (180) (200) = 18,000 Joules!

5. Capacitance of Parallel Plate CapacitorV
V = Ed AND E = Q/(e0A)
(Between two large plates)
So: V =
Recall: CQ/V
So:
(For parallel plate capacitor)
Qd/(e0A) + E - A A
C = e0A/d d
e0=1/(4pk)=8.85x10-12 C2/Nm2

6. Parallel Plate Capacitor
Calculate the capacitance of a parallel plate capacitor made from two large square metal sheets 1.3 m on a side, separated by 0.1 m.
C = e0A/d A A
Here note that this is small number for such a big device. How do they make “real” capacitors? d

7. Dielectric
Placing a dielectric between the plates increases the capacitance.
Dielectric constant (k > 1)
C = k C0
Capacitance without dielectric
The dielectric allows the potential difference between the plates to obtain a higher value and thus store more energy, therefore the capacitance is greater
Capacitance with dielectric

8. Understanding: Parallel Plates+q -q + - d
pull
A parallel plate capacitor is given a charge q. The plates are then pulled a small distance further apart. What happens to the charge q on each plate of the capacitor?
1) Increases 2) Constant 3) Decreases
Remember charge is real/physical. There is no place for the charges to go.

9. +q -q + - d
pull
Understanding
A parallel plate capacitor is given a charge q. The plates are then pulled a small distance further apart. Which of the following apply to the situation after the plates have been moved?
1)The capacitance increases True False
2)The electric field increases True False
3)The voltage between the plates increases True False
4)The energy stored in the capacitor increases True False
C = e0A/d C decreases!
E= Q/(e0A) Constant
V= Ed
U = ½QV

10. Understanding
Two identical parallel plate capacitors are shown in end-view in A) of the figure. Each has a capacitance of C. A ) B )
If the two are joined as in (B) of the figure, forming a single capacitor, what is the final capacitance?
1) 2C
2) C
3) C/2

11. Voltage in Circuits Elements are connected by wires.
Any connected region of wire has the same potential.
The potential difference across an element is the element’s “voltage.”
Vwire 1= 0 V
Vwire 2= 5 V
Vwire 3= 12 V
Vwire 4= 15 V C1 C2 C3
VC2= 7 V
VC3= 3 V
VC1= 5 V

12. Capacitors in Parallel
Both ends connected together by wire
Share Charge: Qeq = Q1 + Q2
Total Cap: Ceq = (Q1 + Q2)/V = C1 + C2
Same voltage: V1 = V2
= Veq
15 V
15 V
15 V
Ceq C1 C2
10 V
10 V
10 V

13. Physics 102: Lecture 4, Slide 13
Parallel Practice
A 4 mF capacitor and 6 mF capacitor are connected in parallel and charged to 5 volts. Calculate Ceq, and the charge on each capacitor.
Ceq = C4+C6
= 4 mF+6 mF = 10 mF
Q4 = C4 V4
= (4 mF)(5 V) = 20 mC
Q6 = C6 V6
= (6 mF)(5 V) = 30 mC
Qeq = Ceq Veq
= (10 mF)(5 V) = 50 mC
= Q4+ Q6
V = 5 V
5 V
5 V
5 V C4 C6
Ceq
0 V
0 V
0 V
Physics 102: Lecture 4, Slide 13

14. Physics 102: Lecture 4, Slide 14
Capacitors in Series
Connected end-to-end with NO other exits
Same Charge: Q1 = Q2 = Qeq
Share Voltage: V1+V2=Veq + +Q -Q +Q
Ceq C1 + - +Q -Q + C2 -Q - -
Physics 102: Lecture 4, Slide 14

15. Physics 102: Lecture 4, Slide 15
Series Practice
A 4 mF capacitor and 6 mF capacitor are connected in series and charged to 5 volts. Calculate Ceq, and the charge on the 4 mF capacitor.
Q = CV
5 V +Q -Q
5 V
0 V +Q -Q + C4 + - -
Ceq +Q -Q + C6 -
0 V
Physics 102: Lecture 4, Slide 15

16. Comparison: Series vs. Parallel
Can follow a wire from one element to the other with no branches in between.
Parallel
Can find a loop of wire containing both elements but no others (may have branches). C1 C2 C2 C1
Physics 102: Lecture 4, Slide 16

17. Comparison: Capacitors vs. Resistors
Capacitors store energy as separated charge: U=1/2QV
Capacitance: ability to store separated charge: C = ke0A/d
Voltage determines charge: V=Q/C
Resistors dissipate energy as power: P=VI
Resistance: how difficult it is for charges to get through: R = r L /A
Voltage determines current: V=IR
Don’t mix capacitor and resistor equations!

18. Electromotive Force Battery + - Maintains potential difference V
Not constant power
Not constant current
Does NOT produce or supply charges, just “pushes” them. + -

19. Understanding
A circuit consists of three initially uncharged capacitors C1, C2, and C3, which are then connected to a battery of emf E. The capacitors obtain charges q1, q2,q3, and have voltages across their plates V1, V2, and V3. Which if any of the following are true?
q1 = q2
q2 = q3
V2 = V3
E = V1
V1 < V2
Ceq > C1 C 2 3 1 E + -
-q2
+q1
-q1
+q3
-q3
+q2 V1 V2 V3

20. Understanding
A circuit consists of three initially uncharged capacitors C1, C2, and C3, which are then connected to a battery of emf E. The capacitors obtain charges q1, q2,q3, and have voltages across their plates V1, V2, and V3. Which if any of the following are true? C 2 3 1 E + -
-q2
+q1
-q1
+q3
-q3
+q2 V1 V2 V3
1) q1 = q2
Not necessarily C1 and C2 are NOT in series.
2) q2 = q3
Yes! C2 and C3 are in series.

21. Understanding
A circuit consists of three initially uncharged capacitors C1, C2, and C3, which are then connected to a battery of emf E. The capacitors obtain charges q1, q2,q3, and have voltages across their plates V1, V2, and V3. Which if any of the following are true? C 2 3 1 E + -
-q2
+q1
-q1
+q3
-q3
+q2 V1 V2 V3
10V 0V
7V??
3) V2 = V3
Not necessarily, only if C2 = C3
4) E = V1
Yes! Both ends are connected by wires

22. Understanding
A circuit consists of three initially uncharged capacitors C1, C2, and C3, which are then connected to a battery of emf E. The capacitors obtain charges q1, q2,q3, and have voltages across their plates V1, V2, and V3. Which if any of the following are true? C 2 3 1 E + -
-q2
+q1
-q1
+q3
-q3
+q2 V1 V2 V3
10V 0V
7V??
5) V1 < V2
Nope, V1 > V2. (E.g. V1 = 10-0, V2 =10-7
6) Ceq > C1
Yes! C1 is in parallel with C23 (Ceq = C1 + C23)