AP Physics C. Electric Circuits III.C

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1 AP Physics C Electric Circuits III.C

2 III.C.1 Current, Resistance and Power

3 The direction of conventional current

5 Suppose the cross-sectional area of the conductor changes.

7 If a conductor has no current, the electrons move randomly at high speeds with no net motion in any direction. If a potential difference is applied across the conductor, the electrons drift in the opposite direction of the field.

9 Ex. The current density in a cylindrical wire with a radius of 2.0 mm is uniform across a cross section of the wire and is 2.0 EE 5 A/m 2. What is the current through the portion of the wire from R/2 to R?

10 If a potential difference is applied across wires of copper and tungsten that have the same geometry, the result is not the same.

15 Check. Rank the three cylindrical copper conductors according to the current they carry if the same potential difference is applied across each.

16 EMF the charge pump

18 An EMF does work to raise charges to a higher potential

19 The Loop Rule and a Series Circuit

20 Series Circuit Only one conducting path The current is the same in each part of the circuit The sum of the potential drops across each resistor is equal to the EMF

23 Ex. A 12 V battery is connected to two 10.0 Ω resistors in series. The battery has an internal resistance of 0.50 Ω. Determine the current in the circuit when the switch is closed. What is the terminal voltage of the battery?

24 Ex. A circuit has two batteries, ε 1 = 4.4 V and ε 2 = 2.1 V connected in series with each other and with a 5.5 Ω resistor. ε 1 has an internal resistance r 1 = 2.3 Ω and ε 2 has an internal resistance 1.8 Ω. A) What is the current in the circuit and B) the terminal voltage across ε 1?

25 Voltmeters and ammeters

26 Parallel Circuits and the Junction Rule

27 Parallel Circuits The potential difference across each branch of a parallel circuit is the same The total current that enters a junction must equal the total current that leaves a junction

29 Ex. For the circuit shown find a) the equivalent resistance b) the current in each resistor c) the drop across each resistor d) and the rate at which heat is dissipated in each resistor.

30 Parallel Plate Capacitors

31 Ex. A 10 nf parallel-plate capacitor holds a charge of magnitude 50 μc on each plate. A) What is the potential difference between the plates? B) If the plates are separated by a distance of 0.20 mm, what is the area of each plate?

32 Spherical capacitors

33 III.C.3 Capacitors in Circuits

34 Capacitors in parallel The potential difference is the same across each capacitor since they are connected to the same battery The total charge is the sum of the charge on each capacitor Capacitors in parallel increase capacitance since the total area increases

36 Capacitors in Series The magnitude of the charge on each capacitor plate is the same The potential drops across each capacitor Capacitors in series decrease the overall capacitance since the charge is constant and the total distance between the plates increases.

38 Capacitors not only store charge they also store electric fields.

39 Calculate the equivalent capacitance for the circuit shown. C 1 = 2.0 μf in parallel with C 2 = 4.0 μf and C 3 = 6.0 μf which are in series with each other.

40 Ex. Find the charge stored in and the voltage across each capacitor in the following circuit given ε = 180 V, C 1 = 30 μf, C 2 = 60 μf and C 3 = 90 μf.

42 Ex. In the diagram shown, C 1 = 2 mf and C 2 = 4 mf. When the switch is open, a battery (not shown) is connected between points a and b and charges capacitor C 1 so that V ab = 12 V. The battery is then disconnected. After the switch is closed, and electrostatic conditions are reestablished, what is the potential difference across each capacitor?

43 Ex. Two capacitors C 1 = 60 μf and C 2 = 24 μf are connected in a loop with a resistor of 20 ohms and an open switch. Initially, C 1 is fully charged and the potential difference across it is 30.0 V. A) Find the current in the resistor immediately after the switch is closed. B) What is the final charge on each capacitor a long time after the switch is closed?

44 Resistance-capacitance (RC) circuits

45 Charging a capacitor. When the switch is closed, the capacitor acts as a conducting wire and the initial current is I = ε/r. But, over time current decreases (transient, not steady state current) and the voltage on the capacitor opposes the EMF of the battery.

46 Current as a function of time finding this almost always means starting with Kirchoff s Loop Rule

48 Q vs. t, I vs. t and V vs. t for a charging capacitor

49 Discharging a capacitor (let s skip a lot of the calculus this time)

50 Q vs. t, I vs. t and V vs. t for a discharging capacitor

51 Ex. In the circuit shown, ε = 20 V, R = 1000 Ω and C = 2.0 mf. If the capacitor is initially uncharged, how long will it take (after the switch is closed) for the capacitor to be 80% charged?

Circuits Practice Websheet 18.1

Circuits Practice Websheet 18.1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. How much power is being dissipated by one of the 10-Ω resistors? a. 24