Physics 1161 Lecture 06 Capacitors Textbook Sections 20

Physics 1161: Lecture 06 Capacitors Textbook Sections 20 -5 – 20 -6

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!

Parallel Plate Capacitor C = 0 A/d 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 A d

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? -q pull - + - 1. Increases 2. Constant 3. Decreases 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? -q pull - + - d + +q pull + 1. Increases 2. Constant 3. Decreases Remember charge is real/physical. There is no place for the charges to go.

-q Preflight 6. 1 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? 40% 1)The capacitance increases C = 0 A/d True C decreases! 50% 2)The electric field increases E= Q/( 0 A) False True False Constant 55% 3)The voltage between the plates increases V= Ed 70% 4)The energy stored in the capacitor increases U = ½QV

Preflight 6. 2 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? 70% 1) 2 C 25% 2) C 5% 3) C/2

Parallel Practice A 4 m. F capacitor and 6 m. F capacitor are connected in parallel and charged to 5 volts. Calculate Ceq, and the charge on each capacitor. Ceq = C 4+C 6 = 4 m. F+6 m. F = 10 m. F Q 4 = C 4 V 4 = (4 m. F)(5 V) = 20 m. C Q 6 = C 6 V 6 = (6 m. F)(5 V) = 30 m. C Qeq = Ceq Veq = (10 m. F)(5 V) = 50 m. C 5 V C 4 0 V Physics 1161: Lecture 4, Slide 8 5 V C 6 0 V = Q 4+ Q 6 V=5 V 5 V Ceq 0 V

Series Practice A 4 m. F capacitor and 6 m. F capacitor are connected in series and charged to 5 volts. Calculate Ceq, and the charge on the 4 m. F capacitor. Q = CV +Q -Q 5 V + + - C 4 + -Q C 6 0 V 5 V +Q - Ceq 0 V

Comparison: Series vs. Parallel Series Parallel • Can follow a wire from one • Can find a loop of wire element to the other with no containing both elements but branches in between. no others (may have branches). C 1 C 2

Preflight 6. 4 A circuit consists of three initially uncharged capacitors C 1, C 2, and C 3, which are then connected to a battery of emf E. The capacitors obtain charges q 1, q 2, q 3, and have voltages across their plates V 1, V 2, and V 3. 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) Ceq > C 1 C 2 E + - V 1 +q 1 -q 1 C 1 +q 2 -q 2 V 2 +q 3 V 3 -q 3 C 3

Preflight 6. 4 A circuit consists of three initially uncharged capacitors C 1, C 2, and C 3, which are then connected to a battery of emf E. The capacitors obtain charges q 1, q 2, q 3, and have voltages across their plates V 1, V 2, and V 3. C 2 E + - V 1 +q 1 C 1 -q 1 35% 1) q 1 = q 2 Not necessarily C 1 and C 2 are NOT in series. 55% 2) q 2 = q 3 Yes! C 2 and C 3 are in series. +q 2 -q 2 V 2 +q 3 V 3 -q 3 C 3

Preflight 6. 4 A circuit consists of three initially uncharged capacitors C 1, C 2, and C 3, which are then connected to a battery of emf E. The capacitors obtain charges q 1, q 2, q 3, and have voltages across their plates V 1, V 2, and V 3. C 2 10 V E + V 1 - +q 1 C 1 -q 1 0 V 45%3) V 2 = V 3 55% 4) E = V 1 Not necessarily, only if C 2 = C 3 Yes! Both ends are connected by wires 7 V? ? +q 2 -q 2 V 2 +q 3 V 3 -q 3 C 3

Preflight 6. 4 A circuit consists of three initially uncharged capacitors C 1, C 2, and C 3, which are then connected to a battery of emf E. The capacitors obtain charges q 1, q 2, q 3, and have voltages across their plates V 1, V 2, and V 3. C 2 10 V E + V 1 - +q 1 C 1 -q 1 +q 2 -q 2 V 2 +q 3 V 3 -q 3 0 V 15%5) V 1 < V 2 50% 6) Ceq > C 1 7 V? ? Nope, V 1 > V 2. (E. g. V 1 = 10 -0, V 2 =10 -7 Yes! C 1 is in parallel with C 23 (Ceq = C 1 + C 23) C 3

Battery • Batteries produce electrons through chemical reactions. • http: //electronics. howstuffworks. com/battery. htm

Recap of Today’s Lecture • • • Capacitance C = Q/V Parallel Plate: C = 0 A/d Dielectric: C = k. Co (k is dielectric constant) Capacitors in parallel: Ceq = C 1+C 2 Capacitors in series: Ceq = 1/(1/C 1+1/C 2) Batteries provide fixed potential difference