Name: ________________________ Class: ___________________ Date: __________
Exam 4--PHYS 202--S15--Induction, AC Circuits
Problem
1. (15 pts) This circuit sits in a magnetic field that varies with time as given by this function:
B(t) = −3t 2 + 4
The circuit is a square and measures 2 meters on a side. One turn of wire in the coil has a resistance of 2 ohms.
a) At t=2 seconds, what is the rate at which the magnetic flux changes?
b) At t=2 seconds, what is the net EMF in the circuit?
c) At t=2 seconds, what is the magnitude and direction of the current?
d) If there were 5 turns of wire in the circuit, what would the current be at t=2 seconds?
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2. (15 pts) Consider this circuit.
a.What is the equilibrium current?
b.How long does it take to reach one-half of this equilibrium current?
c. Sketch the function that shows how current varies with time.
d. Initially, the current is low. Desribe, in 1-2 sentences, what happens in the inductor that keeps the current from
immediately reaching its equilibrium value.
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3. (20 pts) The switch in this circuit is initially closed to point “a.” After a long time, the switch is moved to point
“b.” After flipping the switch describe what happens in the circuit by answering these questions:
a) Describe, in 1-2 sentences, the transfer of energy that occurs between the capacitor and inductor. Sketch a plot
of how the energies vary with time.
b) Initially, which contains the most energy: the inductor or capacitor?
c) What is the frequency and angular frequency of the oscillations?
d) What is the maximum value for the current in the circuit?
e) Calculate a time when the current is at its maximum value.
f) What is the current in the circuit at t=2 seconds?
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4. (15 pts) Check out this LRC circuit. The capacitor has been previous charged by connecting it to a 2 V battery.
a) What is the initial charge on the capacitor (ie., after having been charged)?
b) Sketch a plot of how the charge on the capacitor varies with time.
c) What is the period (in seconds) of the oscillations for this circuit?
d) What is the charge on the capacitor after 10 periods have elapsed?
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5. (10 pts) This figure shows an oscillating function. Draw the phasors for each of the labeled points on the plot. Be
sure to label the phasor with either a-d.
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6. (10 pts) Consider this transformer. The primary voltage comes to the transformer on a wire twisted with 16 turns
around the iron core. The secondary voltage line has 8 turns. a)
a) If the primary voltage is 50 V, what is the secondary voltage?
b) Is this a step-up or step-down transformer?
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7. (15 pts) An RLC circuit has a resistor of 100 Ω, an inductor of 212 mH, and a capacitor of 66 µF; it is powered by
an AC generator that has a maximum EMF of 12 V at a frequency of 60 Hz.
a) What is the maximum, initial current in this circuit?
b) What is the phase constant?
c) Write the expression for the current as a function of time.
d) What is the current at t=0.1 seconds?
e) Draw the phasors that depict the voltage across each component (R, L, and C).
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ID: A
Exam 4--PHYS 202--S15--Induction, AC Circuits
Answer Section
PROBLEM
1. ANS:
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PTS: 1
2. ANS:
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PTS: 1
3. ANS:
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PTS: 1
4. ANS:
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PTS: 1
5. ANS:
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PTS: 1
6. ANS:
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PTS: 1
7. ANS:
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PTS: 1
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