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

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Presentation on theme: "Capacitors! Physics 102: Lecture 4, Slide 1 SPH4UW."— Presentation transcript:

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

2 Capacitance: The ability to store separated charge C=Q/V A B E=E 0 d V = V A – V B = +E 0 d A B d E=2E 0 V = V A – V B =+2E 0 d Potential difference is proportional to charge: Double Q  Double V Q = CV Charge Q on platesCharge 2Q on plates

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 E d Q=CV U =(½) Q V Stores Energy

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

5 Capacitance of Parallel Plate Capacitor V = Ed E = Q/(  0 A) V = Ed AND E = Q/(  0 A) (Between two large plates) So: V = C  Q/V Recall: C  Q/V So: (For parallel plate capacitor) A d A E+ - V  0 =1  k)=8.85x C 2 /Nm 2 C =  0 A/d Qd/(  0 A)

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. A d A C =  0 A/d

7 Dielectric Placing a dielectric between the plates increases the capacitance. Capacitance with dielectric Dielectric constant (  > 1) Capacitance without dielectric C =  C 0 The dielectric allows the potential difference between the plates to obtain a higher value and thus store more energy, therefore the capacitance is greater

8 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? Understanding: Parallel Plates 1) Increases2) Constant3) Decreases Remember charge is real/physical. There is no place for the charges to go. +q-q d pull

9 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 Understanding C =  0 A/dC decreases! E= Q/(  0 A)Constant V= Ed U = ½QV +q-q d pull

10 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 Understanding

11 Voltage in Circuits. Elements are connected by wires. Any connected region of wire has the same potential. V wire 1 = 0 VV wire 2 = 5 VV wire 3 = 12 VV wire 4 = 15 V V C1 = 5 V V C3 = 3 VV C2 = 7 V C1C2C3 The potential difference across an element is the element’s “voltage.”

12 Capacitors in Parallel Both ends connected together by wire C1 C2 Ceq Share Charge: Q eq = Q 1 + Q 2 Total Cap: C eq = (Q 1 + Q 2 )/V = C 1 + C 2 = V eq Same voltage: V 1 = V 2 15 V 10 V 15 V 10 V 15 V 10 V

13 Parallel Practice A 4  F capacitor and 6  F capacitor are connected in parallel and charged to 5 volts. Calculate C eq, and the charge on each capacitor. Physics 102: Lecture 4, Slide 13 C4 C6 Ceq 5 V 0 V 5 V 0 V 5 V 0 V C eq = C 4 +C 6 Q 4 = C 4 V 4 Q 6 = C 6 V 6 Q eq = C eq V eq = 4  F+6  F = 10  F = (4  F)(5 V) = 20  C = (6  F)(5 V) = 30  C = (10  F)(5 V) = 50  C = Q 4 + Q 6 V = 5 V

14 Capacitors in Series Connected end-to-end with NO other exits Same Charge: Same Charge: Q 1 = Q 2 = Q eq Physics 102: Lecture 4, Slide 14 Ceq C1 C Q -Q +Q -Q +Q -Q Share Voltage: V 1 +V 2 =V eq

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

16 Physics 102: Lecture 4, Slide 16 Comparison: Series vs. Parallel Series 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 C1

17 Comparison: Capacitors vs. Resistors U=1/2QV Capacitors store energy as separated charge: U=1/2QV Capacitance: ability to store separated charge: C =  0 A/d Capacitance: ability to store separated charge: C =  0 A/d Voltage determines charge: V=Q/C Voltage determines charge: V=Q/C Resistors dissipate energy as power: P=VI R =  L /A Resistance: how difficult it is for charges to get through: R =  L /A Voltage determines current: V=IR Voltage determines current: V=IR Don’t mix capacitor and resistor equations! Don’t mix capacitor and resistor equations!

18 Electromotive Force Battery 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 C 1, C 2, and C 3, which are then connected to a battery of emf . The capacitors obtain charges q 1, q 2,q 3, and have voltages across their plates V 1, V 2, and V 3. Which if any of the following are true? C 2 C 3 C 1 E + - -q2 +q1 -q1 +q3 -q3 +q2 V1 V2 V3 1)q 1 = q 2 2)q 2 = q 3 3)V 2 = V 3 4)E = V 1 5)V 1 < V 2 6)C eq > C 1

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

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

22 C 2 C 3 C 1 E + - -q2 +q1 -q1 +q3 -q3 +q2 V1 V2 V3 5) V 1 < V 2 Nope, V 1 > V 2. (E.g. V 1 = 10-0, V 2 =10-7 6) C eq > C1 10V 0V 7V?? Yes! C 1 is in parallel with C 23 (C eq = C 1 + C 23 ) Understanding A circuit consists of three initially uncharged capacitors C 1, C 2, and C 3, which are then connected to a battery of emf . The capacitors obtain charges q 1, q 2,q 3, and have voltages across their plates V 1, V 2, and V 3. Which if any of the following are true?


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