Physics 272Lab
Lab 10: Macroscopic View of RC Circuits
Lab 10: Macroscopic View of RC Circuits
OBJECTIVES
In this lab you will
 Use a voltmeter and ammeter to analyze a circuit
 Determine if components of the circuit are ohmic or nonohmic
 Calculate the internal resistance of a battery
 Measure the properties of a capacitor
Built on the foundation of a microscopic understanding of circuits, the macroscopic methods of analyzing
circuits are useful for designing, understanding, or improving circuits at almost all levels of electronics.
In this lab you will use the tools (ammeter and voltmeters), and theories of circuits to analyze the
performance of several circuits and circuits components.
1) Warm-Up Problem
Problem (1) What are the readings on the three meters in the circuit below?
Ammeter 1
10 ohms
Two 1.5 V
Batteries
Voltmeter
20 ohms
Ammeter 2
2) Energy in Circuits
a) Get out the following items for this part of the lab
 1 20 ohm resistor
 1 10 ohm resistor
 1 short bulb and holder
 2 batteries and holder
 6 alligator clips
 1 multimeter
 PASPort voltage probe (see below)
Set up a digital multimeter to be an ammeter, i.e.
b) Connect the black wire to COM.
Physics 272Lab
Lab 10: Macroscopic View of RC Circuits
c) Connect the red wire to the leftmost connector, labeled 10A.
d) Set the dial to 10A.
DON’T USE ANY OTHER SETTINGS AT THIS TIME (YOU COULD BLOW A FUSE IN THE METER).
Next, you will setup your PASPort voltage probe (pictured below) to be a voltmeter. On the lab software
page (http://web.ics.purdue.edu/~jyeazell/Phys272Lab.htm) you’ll find the file titled “Voltmeter.ds”.
e) Right click and download it to your desktop (using a .ds extension).
f) Double click the file on your desktop and it should open.
g) Click START and touch the red lead to the + side of a battery and the black lead to the –
side of that battery.
If it is correctly setup, the digital display on your computer screen should show approximately 1.5 V.
h) Set up the circuit from the warm up problem
i)
Measure the current at the two locations and the voltage difference across both resistors?
i. Do your measurements agree with your warm up calculations?
j) Set up a circuit which is the same as the warm up circuit except replace the 10 ohm resistor
with a short bulb.
k) Wire an ammeter into the circuit so it will read positive amperage.
ii. How do you know which way to wire an ammeter so it reads positive amperage?
l)
Measure the current and the voltage differences across all components of the circuit,
including connecting wires and the ammeter. As you move the voltmeter leads around the
circuit, keep the order of them the same (e.g. red first). Record this data in a neat table in
you work place. Be sure to include units and titles for your columns and rows.
Depending on how you have connected the circuit you should measure approximately eight voltage
differences.
iii. When you attach the voltmeter, you alter the circuit. Why doesn’t the ammeter reading change?
Physics 272Lab
Lab 10: Macroscopic View of RC Circuits
m) Calculate the total voltage change over the entire circuit.
n) Complete this approximate graph of potential (relative to the negative end of the battery)
vs. position around the circuit, showing and labeling the various measured potential
differences.
Part of the graph is drawn for you (see below). Electric field is the (negative) gradient of the potential, so
the slope of this graph should be steep where the electric field is large.
3V
Ammeter
2 batteries
Bulb
20 ohms
CHECKPOINT 1: Ask an instructor to check your work for credit.
You may proceed while you wait to be checked off
3) Ohmic and Non-Ohmic Circuit Components
A resistor is said to be ohmic if the current I through the resistor is related to the potential difference ΔV
across the resistor by the equation I = ΔV/R, where the resistance R is a constant and does not vary with
the voltage difference ΔV. Other resistors whose resistance is not constant (or is a function of potential
difference) are called “non-ohmic resistors.” You will determine if the resistor and the light bulb are
ohmic or nonohmic.
In order to determine if the light bulb and resistor are ohmic, we will reduce the voltage through the
circuit, take voltage and amperage measurements, calculate the resistances of the two components under
the different conditions, and compare the resistances in the 3 volt circuit to a 1.5 volt circuit.
a) Remove one battery from your circuit.
b) Measure and record the current and the voltage differences across the resistor and the bulb.
c) Using I = ΔV/R, find the resistance of the two components in the 3 V circuit and compare
that with the 1.5 V circuit.
i. Is the light bulb ohmic or nonohmic?
Physics 272Lab
Lab 10: Macroscopic View of RC Circuits
ii. Is the resistor ohmic or nonohmic?
iii. If one of the components in nonohmic, what do you think is causing the change in resistance?
CHECKPOINT 2: Ask an instructor to check your work for credit.
You may proceed while you wait to be checked off
4) Time-Dependent Voltage Across A Discharging Capacitor: RC Circuits
You have seen that when a capacitor discharges through a light bulb the bulb starts out bright and then
gets dimmer and dimmer. We will analyze this process in terms of potential.
Consider this circuit containing only a charged capacitor and a resistor.
C= 1 F
+
_
20 Ohms
Voltmeter
The energy conservation equation for this circuit is (assuming the electric field in the connecting wires is
negligible):
ΔVC +ΔVR = 0
The voltage differences across the resistor and capacitor are written as:
ΔVR =-IR
ΔVC =
Q
C
We can use the definition of current to rewrite the potential difference across the resistor.
I=-
dQ
dt
ΔVR =-IR=R
dQ
dt
You can then write the conservation equation for this circuit in this form:
Q
dQ
+R
=0
C
dt
Physics 272Lab
Lab 10: Macroscopic View of RC Circuits
This is a differential equation describing the decrease in charge on the capacitor as a function of time.
a) By using the following guess, show that the solution to this differential equation is,
 t 
Q  t  =Q0exp  RC 
Here Q0 is the initial charge on the capacitor.
As the charge on the capacitor decreases, the voltage across the capacitor also decreases. So, given this
solution for the charge on the capacitor, the voltage across the capacitor must have the similar form.
 t 
V  t  =V0exp 
 RC 
RC is called the “time constant” of the circuit. This is the time at which the voltage difference has
dropped to 1/e or 37% of its original value, V0.
Now you will attempt to measure the value of the capacitance by way of the time constant.
b) Charge the 1 farad capacitor to ~3V by connecting it to your two batteries. Make sure you
connect the positive side of the batteries to the positive side of the capacitor.
c) Remove the batteries and assemble the following circuit, but don’t make the final
connection to the resistor until you are ready to start taking data.
As soon as that connection is made the capacitor will start to discharge.
+
cap
20 ohm
d) On the lab software site, right click and save the data acquisition program
DischargeCapacitor.ds to your desktop with the .ds extension.
(http://web.ics.purdue.edu/~jyeazell/Phys272Lab.htm)
e) Double click the program and it should automatically start software known as Datastudio.
f) Connect the red lead of the PasPort voltage probe to the “+” side of the capacitor and the
black lead to the other side.
g) Complete the connection between the resistor and the circuit and immediately click the
START button.
Physics 272Lab
Lab 10: Macroscopic View of RC Circuits
h) Stop the data collection when the voltage drops roughly to zero (it will take some time).
i)
Use your mouse to highlight all the data.
j) Go to the fit menu and choose Natural Exponent Fit.
k) This fits an exponential to your data (the fit equation has the form A exp( Ct )  B ; note
this C is not capacitance).
l)
In the dialog box, use the constants of the fit to find the initial voltage on the capacitor and
the RC time constant.
Make sure your answer make sense with what you see on the plot.
m) Record the values of V0 and RC .
n) Use your own measured value for the resistance R of the “20-ohm” resistor, and determine
C.
The manufacturing tolerances on these 1F capacitors are not strict. The actual value may range from 0.8F
to 1.8F.
i. Does your result fall in this range?
CHECKPOINT 3: Ask an instructor to check your work for credit. You may proceed while you
wait to be checked off
5) Internal Resistance of a Battery
Due to internal resistance, real batteries do not supply the the same potential difference as their emf. The
voltage of a battery is related to it emf and internal resistance by,
ΔVbat = emf - rint I
Here rint is the internal resistance, ΔVbat is the potential difference across the battery’s poles, and I is the
current in the circuit.
a) Using your 2 resistors, ammeter and voltmeter and assuming that the battery’s internal
resistance is ohmic, find the internal resistance of one of your 1.5 V batteries.
CHECKPOINT 4: Ask an instructor to check your work for credit.