AP Physics C

Electric Circuits III.C

III.C.1 Current, Resistance and Power

The direction of conventional current

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/m2. What is the current through the portion of the wire from R/2 to R?

Ex. Suppose the current density through a cross section varies with the radial distance r as I = ar2 in which a = 3.0 EE 4 A/m4. What is the current through the same outer portion of the wire?

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

EMF – the “charge pump”

An EMF does work to raise charges to a higher potential

The Loop Rule and a Series Circuit

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

Ex. (Princeton Review p. 261) Determine the current in the circuit when the switch is closed. What is the terminal voltage of the battery?

Voltmeters and ammeters

Parallel Circuits and the Junction Rule

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

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.

Parallel Plate Capacitors

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?

Spherical capacitors

III.C.3 Capacitors in Circuits

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

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 must be distributed over a greater area

Capacitors not only store charge they also store electric fields.

Calculate the equivalent capacitance for the circuit shown.

Ex. Find the charge stored in and the voltage across

each capacitor in the following circuit given ε = 180 V, C1 = 30 μF, C2 = 60 μF and C3 = 90 μF.

Ex. In the diagram shown, C1 = 2 mF and C2 = 4 mF. When the switch is open, a battery (not shown) is connected between points a and b and charges capacitor C1 so that Vab = 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?

Resistance-capacitance (RC) circuits

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.

Current as a function of time

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

Discharging a capacitor (let’s skip a lot of the calculus this

time)

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

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 99% charged?

Ex. Capacitors C1 and C2 of capacitance C1 = 6 μF and C2 = 24 μF, respectively, are connected in a circuit shown with a resistor of resistance R = 20 Ohms and a two switches. Capacitor 1 is initially charged to a potential difference of V0 = 30 V and capacitor 2 is initially uncharged. Both of the switches are then closed simultaneously. A) What is the current in R immediately after the switches are closed? B) What are the final charges on each capacitor plate after equilibrium has been reached?