PHYS 202
Lecture 6
Professor Stephen Thornton
February 7, 2005
Reading Quiz
Kirchhoff’s rules are
1. useful to determine the time constant
in a series circuit.
2. required when there are more than 3
resistors in a series circuit.
3. useful to determine currents in
complicated circuits.
4. none of the above.
Answer: 3
None of the other answers seem to be
valid. We use Kirchhoff’s rules to
determine voltages and currents in
complicated circuits.
Last time
¾ Electric current
¾ Electromotive force or EMF
¾ Ohm’s law, V = IR
¾ Resistance and resistivity
¾ Power
¾ Began electric circuits
¾ Resistors in series and parallel
¾ Lots of conceptual quizzes
Today
¾ More conceptual quizzes
¾ Kirchhoff’s rules
¾ Capacitors in series and parallel
¾ RC circuit
¾ Multimeter (leave remainder to lab)
Today’s lecture finishes Ch. 21. Exam
next week on Chs. 19-21
Conceptual Quiz
The light bulbs in the circuit
below are identical with the
same resistance R. Which
circuit produces more light?
(brightness ⇐⇒ power)
1)
2)
3)
4)
circuit 1
circuit 2
both the same
it depends on R
Conceptual Quiz
The lightbulbs in the circuit
below are identical with the
same resistance R. Which
circuit produces more light?
(brightness ⇐⇒ power)
In #1, the bulbs are in parallel,
parallel
lowering the total resistance of the
circuit. Thus, circuit #1 will draw
a higher current,
current which leads to
more light, because P = I V.
V
1) circuit 1
2) circuit 2
3) both the same
4) it depends on R
Conceptual Quiz:
Charge flows through a light bulb. Suppose a wire is
connected across the bulb as shown (called a short
circuit). When the wire is connected,
Short
circuit
wire
1. all the charge continues to flow through the bulb.
2. half the charge flows through the wire, the other half
continues through the bulb.
3. all the charge flows through the new wire.
4. none of the above
Answer: 3
The wire, which has practically zero
resistance, acts as a short circuit. All
the current will flow through the
wire.
Conceptual Quiz:
The circuit below consists of two identical light bulbs
burning with equal brightness and a single 12 V
battery. When the switch is closed, the brightness of
bulb A
1. increases.
2. remains unchanged.
3. decreases.
Answer: 1
The total resistance of the circuit is
less in the second case. We treat the
two resistors in series in the first case.
Because V = IR, I = V/R, the current
is greater with bulb B shorted out.
Go over this yourself.
Go over yourself.
A Single-Loop Circuit
Kirchhoff’s Junction Rule
In +
Out -
The sum of currents meeting at a junction
must be zero. I1 – I2 – I3 = 0 or I1 = I2 + I3
Kirchhoff’s Loop Rule
The sum of
potential
differences
around any
closed circuit
loop is zero.
Our rules:
1) When going from – to + across an emf the
∆V is +. (+ to -, it is -).
2) When going across resistor in direction of
assumed I, the ∆V is -. (Opposite, it is +).
Kirchhoff’s Rules - Example
Show transparency and do calculations.
Conceptual Quiz
The lightbulbs in the
circuit are identical.
When the switch is
closed, what
happens?
1)
2)
3)
4)
5)
both bulbs go out
intensity of both bulbs increases
intensity of both bulbs decreases
A gets brighter and B gets dimmer
nothing changes
Conceptual Quiz
The lightbulbs in the
circuit are identical.
When the switch is
closed, what happens?
1) both bulbs go out
2) intensity of both bulbs increases
3) intensity of both bulbs decreases
4) A gets brighter and B gets dimmer
5) nothing changes
When the switch is open, the point
between the bulbs is at 12 V.
V But so
is the point between the batteries.
batteries If
there is no potential difference, then
no current will flow once the switch is
closed!! Thus, nothing changes.
Follow-up: What happens if the bottom
battery is replaced by a 24 V battery?
24 V
Work Problem 21-52
Capacitors in Parallel
Q1 = C1ε
Q2 = C2ε
Q3 = C3ε
Q = Q1 + Q2 + Q3
Q = Ceqε
Ceq = C1 + C2 + C3
Capacitors in Series
Q
Vi =
Ci
ε = V +V
Q
ε=
1
2
+ V3
Ceq
1
1
1
1
= +
+
Ceq C1 C2 C3
No current,
No charge on C.
Typical RC
Circuit
q (t ) = Cε (1 − e )
q (t = 0) = Cε (1 − 1) = 0
q (t → ∞) = Cε (1 − 0) = Cε
− t /τ
τ = RC
Charge builds up on C.
Charge Versus Time for an RC Circuit
Conceptual Quiz
In the RC circuit we have just been studying,
what is the current at t = 0 and t →∞?
(close switch at T = 0).
1.
2.
3.
4.
5.
t = 0 t→∞
0
0
0
∞
∞
0
∞
∞
None of the above
Answer: 5
The current at t = 0 is not zero or
infinite. It starts out at ε/R and goes
down exponentially to zero. The
current is the rate of change of the
charge. See next slide.
Charge Versus Time
in an RC Circuit
Current Versus Time
in an RC Circuit
Discharging a Capacitor
No current flow.
Capacitor discharges
through resistor.
q(t ) = Qe
−t /τ
Discharging a Capacitor
Do demos
RC Circuit
RC time constant