Physics homework help. Swing Time
Before You Begin
Today’s lab involves making a quantitative study of common circuits that have inductors. This section will
help you review inductance and inductors before you begin.
Since an electric current produces a magnetic field and a magnetic field exerts a force on an electric current
or moving electric charge, it should come as no surprise that a magnetic field can produce an electric current.
Faraday’s law of induction tells us that the emf induced in a circuit is equal to the rate of change of magnetic
flux through the circuit. Combining all these ideas, one might expect that a changing current in one circuit
ought to induce an emf and a current in a second nearby circuit and even induce an emf in itself. The first
situation is known as mutual inductance, when the changing current in one circuit induces a current in a
second circuit. Within a single coil, a changing current induces an opposing emf, so a coil has a selfinductance, L which has units of 1
volt ∙second
ampere
= 1 henry. A coil that has significant self-inductance is called
an inductor.
An inductor stores energy in the magnetic field surrounding its current-carrying wires, just as a capacitor
stores energy in the electric field between its charged plates.
Discussion Questions
While your lab report is an individual assignment, remember that part of your grade for the week is to
participate in Discussions on Canvas with your group members. You are encouraged to discuss any part of
this week’s lab/concepts. You may also want to discuss the following practice problems and questions:
1. At the instant the battery is connected into an LR circuit, like in Task #1, the emf in the inductor has
its maximum value even though the current is zero. Explain.
2. In a battery, when the current is in the same direction as the emf, the energy of the battery decreases,
whereas if the current is in the opposite direction, the energy of the battery increases (as in charging
a battery). Is this also true for an inductor?
Task #1: LR Circuit
For Task #1, you will use a simulation to observe and measure what happens to the voltage across a resistor
and an inductor when they are placed in series in a direct current (DC) circuit.
Go to http://tinyurl.com/tkz8ay8 to find the simulation. Here you should find an LR circuit with the switch
open like in the following picture.
The battery is set to 5V, the inductor is set to 0.85 H (or 850 mH), and the resistor is set to 10 Ω. On the left
side of the screen there is a button to reset the circuit, a button to start/stop the simulation, and various
sliders to change the simulation speed, current speed, and inductance and resistance values. On the bottom is
a scope view that shows both the voltage across the resistor and the voltage across the inductor.
Close the switch and allow current to flow.
A. Describe in words the behavior of the voltage across the resistor in this LR circuit.
B. Look at the scope for the voltage across the inductor. How does it compare to the voltage across the
resistor? Based on the voltage across the resistor and Kirchhoff’s rules, does this make sense? How
do you know?
C. How does the behavior of this circuit compare to an RC circuit? How are they the same and how are
they different?
D. Recall that for RC circuits you were able to define the time (the half-life time) that it took the
voltage to decay to half its original value (?1
2
⁄ = ????2). Can you define a similar time for this
circuit? What would be the value of that (half-life? twice-life?) time for this circuit? Explain how
you determined the value for this time from the voltage graphs.
E. Knowing the units of R and L and using dimensional analysis, can you predict a relation between R
and L that will result in a time value (units of seconds)? Justify your prediction. Using this
prediction, theoretically predict the half-life time for this circuit. How does it compare to the
experimental value you determined in part D?
Task #2: LRC Circuit
For Task #2, you will make a quantitative study of an LRC system. You will do this by investigating the premade circuit simulation, as shown below, at the following url: http://tinyurl.com/vyqerfc. This consists of
an inductor of 0.85 H, a resistor of 10 Ω, a capacitor of 1μF, and a battery at 5 V which can be connected and
disconnected by a switch. The setup is like the previous task. This time the scopes at the bottom are
showing the voltages across the inductor, VL, the capacitor, VC, and the resistor, VR.
A. Predict what happens to VC, VR, and VL as time increases after opening the switch.
B. Open the switch on the LRC circuit. The battery is now disconnected, but the LRC components
make their own independent loop. Describe in words the behavior of the voltages across R, L, and C
in this LRC circuit. Can you think of a mechanical system that has a similar behavior? Describe in
detail how they are similar.
C. Based on Ohm’s law, what can you say about the current in this circuit as a function of time?
Describe it as precisely as possible.
D. Using values from the scope (voltage graph), estimate the time it takes for the system to reach
equilibrium.
a. In a table, record several amplitudes and their corresponding time values over a sufficient
length of time (at least 10 data points).
b. Using Excel or your favorite spreadsheet program, graph the voltage amplitudes as a
function of time, V vs t. Be sure to add a trendline and display your equation. (Hint: it’s
not linear and don’t use a polynomial). Using this graph estimate the time it takes for the
system to reach equilibrium.
c. Estimate the half-life time (the time it takes for the amplitude of oscillations to decay to half
the initial value) for this circuit.
d. Measure the time it takes for the system to oscillate ten times. From this value, determine
the average frequency of oscillation for this circuit.
Using Kirchhoff’s laws, the LRC circuit equation can be written:
?? + ?? + ?? = 0
?
?
2?
??
2 + ?
??
?? +
1
?
? = 0
An exact solution for the charge q in the LRC circuit as a function of time can be written:
? = ?0?

?
2?
?
cos (?

? + ?)
where ?
′ = √
1
??
− (
?
2?
)
2
and ?
′ = 2??
E. Using your measured experimental values, determine the theoretically predicted oscillation
frequency for the LRC circuit. Compare this to your experimental value of the oscillation frequency
of the circuit.
F. Considering your description of the current in the circuit and knowing the relation between charge
q(t) and current I(t), does this solution seem reasonable? That is, does it make sense that the solution
has an exponential contribution and a cosine contribution? Explain why or why not.
G. Try to think back to Lab CE-01: Spring Into Action where you graphed the position of a cart/spring
system as a function of time. How do the graphs seen in this lab compare to those graphs? One
could say for the cart/spring system, that work was initially done by compressing and stretching the
springs. Once released, the energy stored in the springs was converted into kinetic energy of the
cart, which was converted back into spring potential energy. The total energy decreased in time due
to the losses to friction. Write a similar paragraph describing the energy transfers that are occurring
in the RLC circuit. How the energy is initially stored in the circuit? What does the energy oscillate
between? How is the energy lost?
H. Significantly increase the value of the resistor in your circuit (say, by a factor of five). Collect data
for the decay of this system. How did the increased resistance change the total decay time? How did
the increased resistance change the half-life time? How did the increase in resistance change the
frequency of oscillations? Does this make sense based on your previous experiences with oscillating
systems?
Wrap-Up
• Don’t forget to write your Implications section!
• Submit your individual lab report on Canvas. (Make sure to upload all relevant files.)
References
The simulations used in this lab are works by Paul Falstad and were adapted to JavaScript by Iain Sharp. The
program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public
License as published by the Free Software Foundation, either version 2 of the License, or (at your option)
any later version.

Physics homework help