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Transcript
Scenario #1: Bird On A Wire
A typical overhead power line is bare wire at a high potential relative to ground. A local line receives power at
3300 V with respect to the ground; the delivered voltage is slightly less, due to resistance loss in the wire. The
wire is 10 km long, carries a current of 60 A, and has a resistance (made small to limit power loss) of 2.5 Ω.
Multiple Choice Questions (3 points):
1) Approximately how much power is lost due to the resistance of the wire?
A. 9 kW
B. 50 kW
C. 200 kW
D. 4.5 MW
2) If the diameter of the wire is doubled, how does the power lost due to the resistance of the wire change?
(Assume that the current and the voltage stay the same.)
A. It increases by a factor of 2.
B. It stays the same.
C. It decreases by a factor of 2.
D. It decreases by a factor of 4.
Short Answer Question (6 points):
A bird can safely perch on the wire because the voltage drop along the wire leads to a very small potential
difference between the bird’s feet. (Touching a wire while standing on the ground would lead to a different result!)
A large bird is perched on the wire, with feet 6.0 cm apart. Do a quick calculation to see how dangerous this is.
• What is the potential difference between the two ends of the wire?
• What is the electric field in the wire corresponding to this potential difference?
• What is the difference in potential between the bird’s feet?
!
!
© 2014 Brian Jones, all rights reserved. No part of this document may be reproduced without the express written consent of the author.
Scenario #2: Fish In A Field
Multiple Choice Questions (3 points):
The picture at right shows two concentric circular electrodes connected to a power
A B
supply. Consider the potential and the field in the region in between the electrodes.
3) In the lab, you worked with resistive paper with conducting electrodes, and
considered the equipotentials and fields for different electrode arrangements.
+
With the electrodes and power supply voltage as shown,
A. Potential is greater at point A, field strength is greater at point A.
B. Potential is greater at point A, field strength is greater at point B.
C. Potential is greater at point B, field strength is greater at point A.
D. Potential is greater at point B, field strength is greater at point B.
4) Suppose the electrodes are cylinders connected to a 50 V power supply, with a vacuum in between. A proton
is released from the inner electrode. Approximately how fast is it moving when it reaches the outer electrode?
A. 1×103 m/s
B. 1×104 m/s
C. 1×105 m/s
D. 1×106 m/s
!
Short Answer Question (6 points):
If there is an electric field in its tank, a fish will position itself to minimize the potential difference between any
two points on its body. I had a friend who used this principle to do a class demonstration using goldfish in a tank.
He added electrodes connected to a power supply. When the power supply was turned on, the fish moved in the
tank and oriented their bodies, illustrating the structure of the electric field.
Suppose the tank has two electrodes connected to a power supply as shown below. On the diagram below,
• Sketch the equipotentials and the electric field lines.
From the top, the fish have an oval cross section, with one axis wider than the other: !
• Note the most likely position and orientation of a fish in the tank. Where will the fish go? How will it
orient its body?
+
© 2014 Brian Jones, all rights reserved. No part of this document may be reproduced without the express written consent of the author.
a
Scenario #3: Current In A Circuit
If you use a power supply and a network of appropriate
resistors you can create a series of reference potentials in
convenient ratios. This scenario concerns such a circuit, drawn
at right.
5Ω
10 V
c
b
d
5Ω
5Ω
10 Ω
10 Ω
5Ω
Multiple Choice Questions (3 points):
5) What is the equivalent resistance of the circuit?
A. 5 Ω
B. 10 Ω
C. 20 Ω
D. 40 Ω
6) What is the power provided by the power supply?
A. 1 W
B. 5 W
C. 10 W
D. 20 W
Short Answer Question (6 points):
What is the potential at each of the labeled points, a, b, c, d? (Relative to ground, which is 0 V.)
© 2014 Brian Jones, all rights reserved. No part of this document may be reproduced without the express written consent of the author.
Scenario #4: Electricity in the Body
In Chapter 23, we saw a simple electrical model for muscle and nerve cells. Let’s
consider a spherical cell (it’s a simplified model) with conducting fluids inside and out
and an insulating membrane in between.
The capacitance of the cell membrane is 90 pF; the resistance across the membrane is
30 MΩ. Under normal circumstances, the potential inside the cell is 70 mV than the
potential outside. An action potential is triggered if the motion of charges across the
cell membrane changes this potential difference by 15 mV.
Multiple Choice Questions (3 points):
7) If the thickness of the cell membrane is doubled,
A. The resistance of the cell membrane increases, the capacitance increases.
B. The resistance of the cell membrane increases, the capacitance decreases.
C. The resistance of the cell membrane decreases, the capacitance increases.
D. The resistance of the cell membrane decreases, the capacitance decreases.
8) To one significant figure, how much charge must be transferred to trigger an action potential?
A. .1 pC
B. 1 pC
C. 10 pC
D. 100 pC
Short Answer Question (6 points):
A simple defibrillator is a capacitor circuit that is connected by two electrodes to the torso; the capacitor
discharges through the torso, with the resistance of the torso playing the role of R in an RC circuit.
The graph below shows actual data for the voltage across a patient’s torso for a simple defibrillator. The capacitor
was charged to 2500 V.
• What is the resistance of the torso?
• What is the time constant for the discharge?
• What is the capacitance of the defibrillator?
• What is the total energy delivered?
!
I ( A)
50
25
2.0
t ( ms )
© 2014 Brian Jones, all rights reserved. No part of this document may be reproduced without the express written consent of the author.