Tuesday, 26 July 2015
Midterm 2 Review
The following circuits contain capacitors that are charged to 5.0 V. All
of the switches are closed at the same time. After 1 second has
passed, which capacitor is charged to the highest voltage?
Checking Understanding
The following circuits contain capacitors that are charged to 5.0
V. All of the switches are closed at the same time. After 1 second
has passed, which capacitor is charged to the highest voltage?
RC circuits: Charging
• Close the switch, and how does the current change with
time?
RC circuits: Charging
• Close the switch, and how does the current change with
time?
Charging a Capacitor
 Figure (a) shows a
circuit that charges a
capacitor.
 The capacitor charge
at time t is:
where   RC.
 This “upside-down decay”
is shown in figure (b).
Slide 31-114
RC circuits: Charging
• Close the switch, and how does the current change with
time?
Charging a Capacitor
 The equations that describe the capacitor voltage and the
current as a function of time are
© 2015 Pearson
The capacitor is initially unchanged. Immediately
after the switch closes, the capacitor voltage is
A. 0 V.
B. Somewhere between
0 V and 6 V.
C. 6 V.
D. Undefined.
QuickCheck 31.19
The capacitor is initially unchanged.
Immediately after the switch closes,
the capacitor voltage is
A. 0 V.
B. Somewhere between
0 V and 6 V.
C. 6 V.
D. Undefined.
Slide 31-113
The red curve shows how
the capacitor charges
after the switch is closed
at t = 0. Which curve
shows the capacitor
charging if the value of
the resistor is reduced?
QuickCheck 31.20
The red curve shows how
the capacitor charges after
the switch is closed at t = 0.
Which curve shows the
capacitor charging if the
value of the resistor is
reduced?
Smaller time constant.
Same ultimate amount
of charge.
Slide 31-116
Analysis
Consider the following circuit. The capacitor has been
charged to 5.0V and then the switch is closed.
1) What is the voltage across the capacitor after 1 second?
2) What is the charge on the capacitor after 1 second?
3) What is the voltage across the resistor after 1 second?
A circuit – Can you do this one?
What if the 4Ω resistor is
replaced with a capacitor
(the capacitor is initially
uncharged?
 Draw the voltage with
respect to time across the
capacitor and each
resistor.
Solutions on next slide
C
Useful things to remember when analyzing capacitors in circuits:
 Uncharged capacitors act like short-circuits.
 Fully charged capacitors act like a break in the circuit – no
current is flowing to or from the capacitor.
A circuit – Can you do this one?
What if the 4Ω resistor is
replaced with a capacitor
(the capacitor is initially
uncharged?
 Draw the voltage with
respect to time across the
capacitor and each
resistor.
Solutions on next slide
C
A circuit – Can you do this one?
Solutions
Review - Circuits
If the battery lasts for 10hours, and R=20ohms, 5V battery, how
much energy does the battery hold?
●
Note: our classroom discussion holds true, but this is
the quicker path.
Classroom Discussion
• What happens to the
lightbulbs after the switch
is closed?
V=6V, R=2ohms, C=6mF
Classroom Discussion
• What happens to the
lightbulbs after the switch
is closed?
Initially, 1 and 2 are equally
bright. Then 1 get brighter
and 2 eventually goes out.
Now try this one on your own:
•Given the following circuit, explain how the current
will flow just when the circuit is connected and there is
no charge yet on the capacitor, and contrast that with
how the current will flow once the capacitor is fully
charged. Describe what you’ll see in each of the two
light bulbs (will 1 be bright, dark, getting brighter,
dimmer…, what about 2…) from the time the circuit is
first connected to when the capacitor is fully charged.
(The bulbs each have the same internal resistance
R.) Explain your reasoning for full credit.
V=6V, R=2ohms, C=6mF
C
1
2
V
• The capacitor is fully
charged. How long will it
take the voltage to go to
¼ of its original value
once the switch is
opened?
V=6V, R=2ohms, C=6mF
Diameter
3cm
Diameter
1cm
Copper
Aluminum
A 3 cm diameter aluminum wire, conductivity 3.5x107Ω-1m-1 is
connected to a 1cm diameter copper wire with conductivity
6.0x107Ω-1m-1. The current into the aluminum wire is 2.4A.
a) What is the current density in the aluminum wire?
b) What is the current density in the copper wire?
c) How large is the electric field strength in the aluminum wire?
d) How large is the electric field strength in the copper wire?
e) What is the charge density on the interface between the
aluminum and copper wire?
Review – Electric Potential
E
E
Lines more closely spaced for (1) => strongest E-field,
E1>E2=E3
E
A thin, flexible rod of length L with radius R carries a total
charge Q uniformly along its length. The rod is then bent
into a semicircle, as shown in the figure. In this problem
you will need to use integration to find the electric
potential at the center.
1.(6 points) Draw a physical representation of the
situation defining all relevant quantities and symbols
you use.
2.(9 points) Find the electric potential at the center
using integration.
3.(5 points) Provide an evaluation of your result for
part b. What does it tell you about the physics of the
situation? Could this answer be expected without
doing the integration? (Hint: write your answer to part
b in terms of R and not in terms of L)
Full Solution:
Lastly: Can you get from electric potential to Electric field, and visa versa?
See slides from Week 4 Wednesday or HIP4 for some
examples.