Download AP Physics C

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?