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**Physics 102: Lecture 4, Slide 1**

SPH4UW Capacitors! Physics 102: Lecture 4, Slide 1

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**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

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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

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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!

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**Capacitance of Parallel Plate Capacitor**

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

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**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

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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

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**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.

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+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

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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

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**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

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**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

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**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

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**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

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**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

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**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

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**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!

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**Electromotive Force Battery + - Maintains potential difference V**

Not constant power Not constant current Does NOT produce or supply charges, just “pushes” them. + -

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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

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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.

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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

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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)

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