Transcript Capacitors!
SPH4UW Capacitors! Physics 102: Lecture 4, Slide 1 Capacitance: The ability to store separated charge C=Q/V Charge Q on plates Charge 2Q on plates V = VA – VB = +E0 d + E=E0 V = VA – VB =+2E0d + E=2E0 + + + + +A + + + + d - + +A B - + - + d B - Potential difference is proportional to charge: Double Q Double V Q = CV Capacitor Any pair conductors separated by a small distance. (e.g. two metal plates) Capacitor stores separated charge Q=CV Positive Q on one conductor, negative Q on other + Net charge is zero + • Stores Energy U =(½) Q V + E - + - + d 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! Capacitance of Parallel Plate Capacitor V V = Ed AND E = Q/(e0A) (Between two large plates) So: V = Qd/(e0A) Recall: CQ/V C = e0A/d So: +E A A (For parallel plate capacitor) d e0=1/(4pk)=8.85x10-12 C2/Nm2 - 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 (8.85 1012 )(1.3)(1.3) C (0.1) 1.5 10 10 F A A d Dielectric Placing a dielectric between the plates increases the capacitance. Dielectric constant (k > 1) C = k C0 Capacitance with dielectric 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 Understanding: Parallel Plates -q pull - + d + - + - + +q 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. -q Understanding pull - + d + - + - + +q pull 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 C = e0A/d False True False C decreases! 2)The electric field increases E= Q/(e0A) True Constant 3)The voltage between the plates increases True False V= Ed 4)The energy stored in the capacitor increases U = ½QV True False Understanding Two identical parallel plate capacitors are shown in endview in A) of the figure. Each has a capacitance of C. B) A) 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 C e0 A d 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 C1 VC1= 5 V Vwire 2= 5 V Vwire 3= 12 V C2 VC2= 7 V Vwire 4= 15 V C3 VC3= 3 V Capacitors in Parallel Both ends connected together by wire • Same voltage: V1 = V2 = Veq • Share Charge: Qeq = Q1 + Q2 • Total Cap: Ceq = (Q1 + Q2)/V = C1 + C2 15 V 15 V 15 V C1 C2 10 V 10 V Ceq 10 V 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 5V C4 0V = (10 mF)(5 V) = 50 mC = Q4+ Q6 5V V=5V C6 0V Physics 102: Lecture 4, Slide 13 5V Ceq 0V Capacitors in Series Connected end-to-end with NO other exits Same Charge: Q1 = Q2 = Qeq • Share Voltage: V1+V2=Veq 1 1 1 Ceq C1 C2 +Q -Q +Q -Q + + + ++ ++ +Q C1 + - - - + ++ + + Ceq C2 -Q - - - Physics 102: Lecture 4, Slide 14 - 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. 1 1 1 1 Ceq C 4 C6 1 1 2.4 m F 4m F 6m F Q = CV Q4 Q6 Qeq CeqV ( 2.4m F (5V 12mC 5V +Q -Q +Q -Q + C4 + + -Q Ceq 0V C6 0V 5V +Q Physics 102: Lecture 4, Slide 15 Comparison: Series vs. Parallel Series • Parallel Can follow a wire from one element to the other with no branches in between. • Can find a loop of wire containing both elements but no others (may have branches). C1 C1 C2 Physics 102: Lecture 4, Slide 16 C2 Comparison: Capacitors vs. Resistors Capacitors store energy as separated charge: U=1/2QV Capacitance: C = ke0A/d Voltage determines charge: V=Q/C Resistors dissipate energy as power: P=VI ability to store separated charge: 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! Electromotive Force Battery + Maintains potential difference V Not constant power Not constant current Does NOT produce or supply charges, just “pushes” them. 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? 1) q1 = q2 2) q2 = q3 3) V2 = V3 4) E = V1 5) V1 < V2 6) Ceq > C1 C2 E + - V1 +q1 -q1 C1 +q2 -q2 V2 +q3 V3 -q3 C3 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? C2 E + - V1 +q1 -q1 C1 +q2 -q2 V2 +q3 V3 -q3 1) q1 = q2 Not necessarily C1 and C2 are NOT in series. 2) q2 = q3 Yes! C2 and C3 are in series. C3 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? C2 10V E + V1 - +q1 C1 -q1 0V 3) V2 = V3 4) E = V1 Not necessarily, only if C2 = C3 Yes! Both ends are connected by wires 7V?? +q2 -q2 V2 +q3 V3 -q3 C3 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? C2 10V E + V1 - +q1 C1 -q1 7V?? +q2 -q2 V2 +q3 V3 -q3 0V 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) C3