Note: I typed this in Word and the subscripts and the symbol for emf got messed up. Where it says VT, or IT, etc, the T should be a subscript.

Circuits



Concepts and Equations

- Circuits are composed of electrical elements (capacitors, resistors, batteries, wires, and solenoids in LC and LCR circuits).
- Emf – potential difference between the terminals of a device that transforms one type of energy into electrical energy.
- Internal resistance
Terminal voltage – Vab = E - Ir
- Voltage Drop
- Series circuits – connected end to end
VT = V1 + V2
IT = I1 = I2
RT = R1 + R2
- Parallel circuits – current from the source is split and branched off
VT = V1 = V2
IT = I1 + I2
1/RT =1/R1 + 1/R2
- RC Circuit – a circuit that contains both resistance and capacitance

t = 0
t = much later
t = in between
t = all the time
q = 0
qf = Q = VC
V = (dq/dt)R + q/C
V = vc + vr
vc = 0
vc = V
q = Q(1-e-t/RC)
vr = iR
vr = V
vr = 0
vc = V(1-e-t/RC)
vc = q/C
I = (V/R)
i = 0
i = V/R e-t/RC
V = iR + q/C


vr = V e-t/RC


- Kirchhoff’s Rules – Used to deal with complicated circuits
Junction rule, Loop rule

Other Equations
C = kε0A/d
R = ρl/A
V = IR
P = IV
I = ΣnqVA
J = ΣnqV
J = I/A

Investigation

We did a lab where we measured the voltage across a battery and resistor as the battery was charging up and as the battery was discharging.


Multiple Choice

1. What is the terminal voltage for a battery with an internal resistance, r, of .900Ω and an emf of 8.50V when the battery is connected in series with a 68Ω resistor?
a) 0.838V
b) 0.125V
c) -52.7V
d) 52.7V
e) 8.39V

2. Three light bulbs are connected in series and each bulb has a resistance of 1Ω. What is the equivalent resistance of the circuit?
a) 1Ω
b) 2Ω
c) 3Ω
d) 1/3Ω
e) 2/3Ω

3. Three light bulbs are connected in parallel and each bulb has a resistance of 2Ω. What is the equivalent resistance of the circuit?
a) 3Ω
b) 2/3Ω
c) 3/2Ω
d) 1/2Ω
e) 1/3Ω

4. Circuit.jpgWhat is the equivalent resistance of this circuit if the two inner resistors have a resistance of 2Ω and the resistor on the left has a resistance of 1Ω?
a) 1Ω
b) 2Ω
c) 3Ω
d) 1/2Ω
e) 1/3Ω

5. A capacitor that can hold a maximum charge of 99A is being charged. At t=RC, approximately, what is the charge on the capacitor?
a) 66A
b) 33A
c) 99A
d) 50A
e) Cannot determine unless the value of the resistance is given.

Open Response

An RC circuit has a total resistance of 2Ω, a total capacitance of 5F, and a voltage of 60V.

Q = total charge, q = charge at a given time, t = time, Vc = voltage of the capacitor, Vr = voltage of the resistor, i = current at a given time, I = total current.

a) What are the values of q, Vc, Vr, and i at t = 0?
b) At t = much later?
c) At t = in between?
d) At t = all the time?
e) Show mathematically how the charge and voltage can be approximated when t = RC.


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