Homework, Chapters 6 and 7
1. In this figure, the magnetic field through the loop changes according to this
function: ‫ = ܤ‬6.0‫ ݐ‬ଶ + 7.0‫ݐ‬, where B is in tesla and t is in seconds. The radius of
the loop is 1.5 cm, and the resistor is 3.0 ohms. What is the magnitude of the
EMF induced at t=2.0 s? What is the magnitude and direction of the current?
2. A square wire loop with 2.00 m sides is perpendicular to a magnetic field as
shown. One-half of the loop is in the B-field, which varies with time according to
this function: ‫ܤ‬ሺ‫ݐ‬ሻ = 0.0420 − 0.870‫ݐ‬. The loop contains an ideal battery with
ߝ = 20.0 V. What is the net EMF and the magnitude and direction of the current?
What if there are now 10 turns of wire instead of just one. What is the EMF &
current?
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Chapter 7, Electromagnetic Oscillations
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3. What is the magnetic flux through the loop shown in this figure?
4. Consider this circuit.
a. What is the equilibrium current?
b. How long does it take to reach that current?
c. How long does it take to reach one-half of this equilibrium current? Write
the loop rule for this circuit and show that the sum of the potentials at this
time is equal to zero. When it is at this current, what is the energy stored
by the inductor?
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Chapter 7, Electromagnetic Oscillations
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5. Consider this circuit. Initially, the capacitor is fully charged by a 12 V battery,
and no current flows in the circuit.
a.
b.
c.
d.
e.
f.
Discuss how the energy on the capacitor and inductor changes with time.
When is the first instance that the current in the circuit is zero?
When is the current at its maximum value?
What is the angular frequency for the oscillating current?
What is the charge on the capacitor at t=2s?
What is the current in the circuit at t=2s?
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Chapter 7, Electromagnetic Oscillations
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6. Consider this circuit. The switch is in position A for a long time; then, it is
flipped to position B. What are the (a) frequency and (b) current amplitude of the
resulting oscillations?
7. A single loop circuit has a 7.20 Ω resistor, 12.0 H inductor, and a 3.20 µF
capacitor. Initially, the capacitor has 6.20 µC, and the current is zero. Calculate
the charge on the capacitor N complete cycles later for (a) N=5, (b) N=10, and (c)
N=100.
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Chapter 7, Electromagnetic Oscillations
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8. A 50.0 Ω resistor is connect with an AC power source. The amplitude of the
EMF is 30.0 V. What is the amplitude of the alternating current if the frequency
of the EMF is (a) 1.00 kHz and (b) 8.00 kHz?
9. An AC power supply with EMF ε=εM=sin(ωdt), with εM=25.0 V and ωd=377
rad/s. The power supply is connected to a 12.7 H inductor. (a) What is the
maximum value of the current? (b) When the current is at a maximum, what is the
emf of the generator? (c) When the emf of the generator is -12.5 V and increasing
in magnitude, what is the current?
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Chapter 7, Electromagnetic Oscillations
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10. Consider this function. Draw the phasors for points a-d.
11. Consider this transformer. The primary voltage comes to the transformer on a
wire twisted with 4 turns around the iron core. The secondary voltage line has 8
turns. If the primary voltage is 100 V, what is the secondary voltage? Is this a
step-up or step-down transformer?
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Chapter 7, Electromagnetic Oscillations
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12. An RLC circuit has a resistor of 100 Ω, an inductor of 200 mH, and a capacitor of
3 µF; it is powered by an AC generator that has a maximum EMF of 24 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 for VL, VR, and VC and be able to discuss which follow and
which lead the EMF of the generator.
f) What is the resonant frequency of this circuit? What is the current at this
resonant frequency?
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Chapter 7, Electromagnetic Oscillations
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