HLab 7

Sensitivity of a galvanometer


Goal
To determine the current
required for fullscale deflection of a galvanometer
Equipment
Digital multimeter
Galvanometer (from analog multimeter)
Breadboard
2 1kiloohm (kW) resistors
6 100kiloohm (kW) resistors
6V battery pack
Clip leads
Summary
of Method
You'll first connect a
series circuit of the 2 1kW
resistors (referred to as the "load resistance") and the battery pack.
Then you'll create your own voltmeter to measure the potential
difference across one of the resistors. The voltmeter will be composed
of a galvanometer in series with a chain of 100kW
resistors (this chain is referred to as the galvanometer's "multiplier
resistance"). You'll measure the galvanometer deflection as a function
of total voltmeter resistance. For comparison to the analog meter
results, you'll also use the digital multimeter to measure the
potential difference.
You'll use your
measurements together with theoretical circuit equations to determine
the current required to deflect the galvanometer full scale. You'll
then check your work by changing the load resistance, calculating the
multiplier resistance required for fullscale deflection, and then
testing the result.
Prelab
Read the entire lab
instructions and format your lab book accordingly.
Since detailed lab procedures are listed below, you may simply refer to
these procedures in the Method section of your report.
Important:
In your derivations, it's very important that you use the symbols
defined in step 2 below. It's also important that you express
your work clearly. Write in a large font, list equations one
below the other, and leave extra space between them for the instructor
to note corrections. If you don't follow these guidelines, you
may have to rewrite your work so that it can be checked.
 Review HRW 28.6 and 28.7.
 Make a diagram of the circuit described in Summary of Method
above. In addition to the components indicated, include the
galvanometer with its multiplier resistance. Denote the series
load resistors as R_{1} and R_{2} (don't assume they're
equal), the multiplier resistance as R_{m}, and the
galvanometer coil resistance as R_{g}. R_{1} will be
the resistor across which the voltmeter is placed. We're using fresh
batteries so that we can ignore their internal resistances in
comparison to the load resistances. (For simplicity, you may use the
symbol R_{v} to represent the combined galvanometer and
multiplier resistances.)
 Using Kirchhoff's Laws (aka loop
rules and junction rules), solve for the galvanometer current in terms
of the given resistances and the terminal voltage of the battery.
Express your result in simplest form. This equation will be used later
to solve for the galvanometer current using measurements of the other
quantities.
 Rearrange your equation from 3) to obtain an equation for the
multiplier resistance. This will be used later to solve for the
multiplier resistance necessary to give a fullscale deflection for a
given load resistance.
About
recording your data, results, and calculations: Use
your lab journal as intended, which is as a journal. Keep clear
and complete labeled records of your work. Evaluation of
your work depends partly on how easily the instructor can find
information and interpret what you did.
Method
Important: Don't connect the circuit to the
battery until the instructor has checked your circuit. The
galvanometer can easily be damaged by sending too much current through
it. If you burn out your galvanometer, your experiment is over.
About
your work: You'll work with a group of 1 or 2 other
students. You'll build the same circuit and collect the same
data. However, each student is expected to keep their own records
and do their own calculations.
 Your galvanometer has a letter (AF) on the face of the
meter. Record this letter.
 Use the digital multimeter to measure the resistances of all the
resistors, the resistance of the galvanometer coil, and the terminal
voltage of the battery pack. Record and label these values clearly,
using the same symbols as defined previously.
 Construct the circuit described previously. Use a chain of 6 100kW resistors as the multiplier resistance.
 Ask the instructor to check your circuit.
 If the circuit checks out, connect the battery. If the
galvanometer deflects the wrong direction, reverse the battery leads.
You should get a small positive deflection.
 Construct a table with 5 columns. The first three columns will be
Multiplier Resistance, Galvanometer Deflection (read on the 05 scale
to the nearest tenth of a minor division), and Digital Voltmeter
Reading. Be sure to record measured values (as opposed to nominal
values). The next 2 columns will be reserved for calculations. Label
these Equivalent Resistance and Galvanometer Current.
 Reduce the multiplier resistance by one 100kW resistor. Record the new set of
measurements.
 Repeat the previous step until the galvanometer deflection is
between half and fullscale. Don't reduce the multiplier
resistance beyond this point. Otherwise you run the risk of damaging
the galvanometer.
 Disconnect the battery. Go on to the Calculations.
Important: Keep
all your components in an identifiable location in case it's necessary
to retake data later.
Calculations
Significant figures are
very important in this lab. Be wary of rounding errors.
Number your responses as
given below.
 What is the percentage change in the galvanometer deflection over
the full range of multiplier resistances used?
 Compare the result of 1) to the percentage change in the digital
meter reading over the same range of multiplier resistances. Explain
any differences qualitatively.
 Calculate the equivalent resistance of the entire circuit
(including galvanometer branch), using your data for your highest
multiplier resistance. Start with a formula and show your substitutions.
 Using one of your prelab equations and your data for the highest
multiplier resistance, calculate the galvanometer current. Start with
the equation, show your substitutions, and give the final result.
 Record the values calculated in the previous two steps in your
table.
 Repeat your calculations of current and equivalent resistance for
the other multiplier resistances. Don't show these calculations. Simply
record them in the table.
 In Graphical Analysis, plot a graph of Galvanometer Current vs.
Scale Reading. Fit a straight line to the data. Document your graph and
data table clearly. Record your name and your partners' names in a text
box. Also write in the text box the equation of fit with physics
variables and numerical values of the coefficients with units.
Save the file with the name hlab7X.ga3, where you replace X
with the letter of your galvanometer. Submit one file per lab
group by emailing it to the instructor. Also email a copy of the
file to every group member. This file must be submitted during the
lab period unless you make other arrangements with the instructor.
 Using the equation of fit from 7), calculate the current required
for fullscale deflection of the galvanometer. We will call this the
sensitivity of the meter.
Check
The purpose of this last
section is to check your work.
 Measure the battery voltage and record the value. If this value
has changed significantly from the value that you found previously, be
sure to use the new value in the following.
 Ask the instructor for a new resistance value for R_{1}
in the range of 210 kW. Using an
equation from the prelab and the calculated galvanometer sensitivity,
calculate the multiplier resistance needed for fullscale deflection of
the galvanometer. Assume that all other circuit components (resistors
and power supply) remain the same. Remember that the multiplier
resistance doesn't include the galvanometer resistance.
 Now replace the existing R_{1} in the circuit with the
new one. Replace the multiplier resistance with the value calculated in
the previous step. This may require finding a combination of resistors
that will yield the desired value to 3 significant figures.
 Connect the battery to the circuit and record the galvanometer
deflection.
 Calculate the percentage difference between the measured
deflection and the expected value of 5.00.
 Check with the instructor about whether your percentage
difference is acceptable.
Discussion
and Conclusion
Summarize what you did, how
you did it, and what you found in this lab. Discuss errors that could
contribute to differences between experimental and theoretical
values. Submit your lab book by the due date.