Download PHY 142L Spr 2016 Lab 2

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DC Circuits and Capacitors
Electric circuits can be designed to perform an incredible array of functions that we have come to rely on in daily life.
From the distribution of power through transmission lines and the wiring of a household electrical system to the
submicron scale circuits in computer chips, all circuits are just arrangements of a few types of elements: resistors,
capacitors, inductors, diodes, transistors, and of course the wires that connect them. In this lab, we will examine some
of the roles that resistors and capacitors can play, as these are the elements we can readily understand at this point in the
course. (The theory of inductors requires an understanding of magnetic fields, and the theory of diodes and transistors
requires a more advanced understanding of semiconductor materials.)
Resistors can take many forms. In this lab we will use light bulbs as resistors because they give a direct visual
indication of the amount of current passing through them: for any given bulb, the brighter bulb, the greater current.
(There is a technical definition of “brightness” that corresponds fairly well to the common meaning of the term. It is a
measure of the power radiated by the bulb, which is proportional to the square of the current.) Resistors are often
placed in a circuit just to control the electric potentials at different points, but are also often output elements where
electrical power is converted to desired light or heat.
Capacitors function as storage units, holding electrical energy and charge that can be used to drive electric currents at a
later time. The energy is stored in an electric field establish by a voltage difference across the plates of the capacitor. In
this lab, we will study the effect a capacitor on the behavior of the current in a circuit designed to make a bulb “flash”
once. We will then study how the amount of energy stored in a capacitor depends on the voltage across it by observing
how high a weight can be lifted using the stored energy when the capacitor is charged at different voltages.
Power supplies are complex devices designed to hold the potential difference between two terminals at specified
values. They run on electrical energy supplied by another source (e.g., the utility lines carrying electrical power
from a generator), and can be thought of as ideal batteries. We can think of one terminal as an inexhaustible
source of charge that can flow through connected wires and devices and is then be deposited at the other
terminal, where work is then done on the charge to return it to the source terminal. We say that the power supply
provides an electromotive force (emf) that drives charge from one terminal to the other. [NOTE: Emf is not
actually a force! It has units of electric potential, or voltage.]
The flow of positive charge is called the electric current in the circuit. (In typical cases, the particles that are
actually flowing are electrons, which have negative charge. By convention, we define the direction of the
electric current to be opposite to the direction the electrons move.) In the case of direct current (DC), the
voltage of the power supply is held fixed. For many applications, one uses alternating current (AC), where the
voltage difference between the two terminals oscillates sinusoidally. For example, the power supply for
household electrical devices (the local power generating plant) generates a voltage difference between the two
wires of a typical wall outlet that oscillates 60 times per second with a maximum of +165 Volts and a minimum
of -165 Volts.
Circuits consist of components connected with wires to a power supply. Wires have very little resistance (effectively
zero for our purposes). We can treat them as perfect conductors, and we know that the electric potential of perfect
conductor is the same everywhere on the conductor. Thus we know that in any circuit, the voltage at one end of an
unbroken wire is the same as the voltage at the other end.
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Experiment
In this experiment, you will be using a heavy-duty laboratory power supply. This supply has terminals for both
alternating current (AC) and direct current (DC), but we will use only the DC terminals.
The DC terminals may be adjusted between 0 and 24 Volts. However, this laboratory uses tiny light bulbs, which burn
out easily. Your power supply has been pre-adjusted, and you will have no need to make any changes during this
laboratory. Notice that the power supply also has a “Current Adjust” knob. This is actually a current limiter circuit,
and the knob will change the threshold of the maximum current allowed to flow in the circuit. It is usually used as a
safety feature to prevent too much current from flowing in the event of a short circuit. [A “short circuit” arises when
one terminal of a power supply is connected directly to the other by a wire or any other excellent conductor. Because R
is very small, a given V produces a huge I, which can cause damage.]
I. A series circuits
Construct a two-bulb circuit with identical bulbs connected as shown. Bulbs connected in this way are said to be
in series. An charged particle must pass through a series of objects to get from one terminal to the other.
A. Compare the brightness of the two bulbs. Should one be brighter than the other? (If so, which one? If not,
why not?)
B. Switch the wires connected to the power supply so as to reverse the direction of the current through the
bulbs. Does the brightness of the bulbs change?
C. Compare the brightness of each bulb in the two-bulb series circuit with that of a bulb in a single-bulb circuit. How
does the current through a bulb in a single-bulb circuit compare with the current through the same bulb when it is
connected in series with a second one? Explain.
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II. Parallel Circuits
Construct a two-bulb circuit of identical bulbs with the terminals
connected together as shown. Bulbs connected in this way are
said to be in parallel. There are two parallel paths by which
charges can move from one terminal to the other.
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A. Compare the brightness of the two bulbs in this circuit.
1. How do the currents through two bulbs compare?
2. Describe the current in the entire circuit, specifying its relative magnitude and direction in each
segment of wire.
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B. Predict how the brightness of bulb 1 will change if you remove bulb 2 from the circuit.
C. Disconnect bulb 2 and observe what happens to bulb 1. Does this agree with your prediction? Explain
the observed effect using the vocabulary of voltage drops and currents.
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III. Discharging a capacitor through a light bulb
In this lab you will use a large capacitor (1 Farad), which can store a substantial amount of energy. As for any
capacitor, however, the amount of energy one can store is limited because applying too big a potential difference
between the plates will cause material failure. For the capacitors used in this lab, the maximum potential
difference is 5 Volts.
To protect from wear and tear, the capacitor is housed inside a box (schematically indicated by the grey rectangle
in the figure below). Each box has a control switch that can be pressed in two directions. When you release the
switch, it will turn off immediately; this is for safety. When you press the switch towards one of the two
terminals on top of the box, you complete a circuit that allows the charge on the capacitor to flow through
whatever device is connected to the terminals. We say the capacitor discharges as it drives the current. You can
also press the switch in the opposite direction, towards the long wire that extends from the back of the box. The
ends of this wire should be connected to the terminals of your power supply, and so holding the switch in this
direction will charge the capacitor.
Your power supply has an AC (Alternating Current) section and a DC (Direct Current) section. During this lab,
we will only use the DC section, which is on the left side of the supply and is demarcated by a red and a black
banana socket. Please do not adjust the voltage to more than 4V during this lab. (It will ruin the capacitors!)
The DC supply has a current limiter adjustment, which limits the maximum current in your circuit. Please do
not change this setting.
Construct the circuit shown in the diagram at right. Hold
the switch to charge the capacitor from the power supply,
then open the switch. Finally, close the switch the other
way to connect the capacitor to the bulb. Observe what
happens to the bulb and describe it. Write a qualitative
explanation of your observations in terms of the changing
currents through different wire segments and voltages at
different points in the circuit.
Power
supply
Bonus question: (Do this only after you have completed the entire lab.)
Connect the light bulb as shown at right. What will happen when you
close the switch? Do it, then describe qualitatively your observations.
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Power
supply
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Part 2: Energy stored in a capacitor
We now replace the light bulb in the first (parallel) circuit above with an electric motor, which is a device that
converts electrical energy into mechanical energy. For now, the conversion process will remain mysterious, but
we will study the relevant physics later in the semester.
A charged capacitor can retain most of its energy for up to several hours. However, some charge will begin to
leak off immediately, and so (for the sake of collecting good data in this lab) you should always charge your
capacitor immediately before you use it.
Your electric motor has two long wires, which terminate in banana plugs. These banana plugs can be connected
to the terminals on top of your capacitor box. If necessary, you can reverse the motor by reconnecting the wires
so that the current flows in the opposite direction.
Our goal in this lab is to study how the energy stored in a capacitor depends on the voltage used to charge it up.
We will do this by using the stored energy to run a motor that lifts a known weight.
Using the electric motor
Before putting the capacitor to work, take a moment to familiarize yourself with the operation of the motor by
hooking it up directly to the power supply: First, tie a long (~2 meter) length of string to the plastic pulley, and
tie a small loop in the free end of the string so that you can hang masses. Then turn on the power supply and
adjust it to 4V. (Please do not exceed 5V during this lab. Your TA has been instructed to subtract 3 points from
your score if you do). Now connect the motor's wires directly to the power supply, and try lifting up a 100g
mass. Try this at several different voltage settings between 1.5V and 5V.
Using the energy in the capacitor to lift a weight
Hang 100 grams of mass on your string, and let out enough length so that the mass nearly touches the floor.
Construct the same circuit as the parallel one above, replacing the light bulb with your motor.
You should be able to charge the capacitor by holding the toggle switch down in the correct direction. When you
toggle the switch in the other direction, the capacitor will drive your motor.
Set the power supply to 2V, and charge the capacitor. As you do this, observe the current readout on your power
supply. If you miss what happens, discharge your capacitor through your motor and try again.
1. Describe what happens to the current as a function of time while the capacitor charges, and explain the
behavior.
2. What is the voltage across the capacitor when the current goes to zero?
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Prediction: How high above its initial position do you think your motor can lift a100g mass using only the
energy stored in the capacitor? Take a guess without worrying too much about how accurate it might be, and
write it down.
Perform the experiment.
3. How far did the motor raise the mass before it stopped turning?
Now we would like to figure out how much energy was stored in the capacitor, but there are two complications
that we must take into account.
i. The motor does not convert electrical power to mechanical power with perfect efficiency. Some energy
is lost to heat through mechanical friction and electrical resistance. We will take the efficiency of the
motor to be 𝜂 = 0.3. This is the fraction of the input electrical power that is converted to output
mechanical power.
ii. The efficiency of the motor gets much lower when the voltage applied to it drops below about 0.9 V, and
the motor actually stops turning altogether when the applied voltage drops below about 0.7 V. This
means that the weight stops rising before all of the energy in the capacitor is used up. We will let Estop
represent the energy left in the capacitor when the motor stops turning. That is, the initial energy E in the
capacitor is approximately Estop plus whatever energy was used to lift the weight.
4. In terms of the height the mass was raised and the unknown quantity Estop, write an expression for the energy
originally stored in the capacitor.
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Prediction:
On the axes below, draw a curve showing (in a general way) a prediction for the relationship
between the voltage used to charge the capacitor and the final height of the mass.
Final height
0.7 V
Initial Voltage
Measure the vertical displacement of a 100g mass for 5 different voltages used to charge the capacitor in a range
between 2V and 3V, and plot your data. Remember to turn in your graph with your report! Remember also that
your capacitor loses charge slowly, so you will obtain the best data if you run the motor right away after charging
the capacitor. Take the data twice to make sure it is reproducible.
5. Examining your plot of height vs. voltage, what shape of curve does this seem to be? Explain your reasoning.
How did your prediction pan out?
6. [The big one!] How does the energy stored in your capacitor depend on the voltage used to charge it up?
Write a formula for the stored energy as a function of V.
7. How would you expect your formula to change if you used a different capacitor?
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