Download Lab 4. Magnetic field and currents: an ammeter

LAB
Part
271
4: MAGNETIC FIELD AND CURRENTS: AN AMMETER
3: Circuit
model of surface
resistivity
Solder at least 25 identical resistors in a square mesh as shown in Fig.L3.2b. (A lab technician
or the instructor may do this ahead of time for you.) This is a circuit model of a thin layer of
resistive material. Imagine you insert a current at a point in the middle of the mesh. Draw
the current paths. What do they look like as the mesh becomes finer and larger?
L3.8. Using an ohmmeter, measure the resistance between adjacent points, such as A and B,
at different places across the mesh (i.e. in the center and closer to the edges). What resistance
are you expecting to approximately measure in the middle of the mesh based on your prelab
problem PL3.4?
L3.9. How do your measurements compare with the calculation for different pairs of adjacent
points across the mesh?
L3.10. If you have time and you are interested, repeat measurements and calculations for
problem P11.16. How would you make a discrete model for volume, not surface, resistivity?
Conclusions:
1. Resistivity and surface resistivity can be measured using a four-point probe voltage and
current measurement. The calculation of the resistivity from this measurement is based
on superposition of two currents.
2. The method of measurement is slightly different for thick samples and thin layers, as well
as for high-resistivity and low-resistivity (high conductivity) materials.
3. We can make a circuit model (mesh of identical resistors) of homogeneous resistive layers
as well as resistive blocks of material. To calculate the value of resistance between any two
points in the circuit model, we can use the two-point probe analysis based on superposition
instead of a relatively complicated circuit analysis.
Lab 4. Magnetic
field and currents:
an ammeter
Background:Circuits, Chapter 12 in Introductory Electromagnetics
A current produces a magnetic field, which can in turn produce a force on either a magnet or
another wire with current flowing through it. In this lab, we will produce a static magnetic
field with a dc current flowing through a dense spiral winding, usually called a solenoid. The
magnetic force will act on a small magnet (a compass needle). By measuring the force on the
small magnet, we can measure the intensity of the current flowing through the solenoid.
Purpose:
to see how current produces a magnetic field, and to learn how to measure the
current by measuring magnetic force. The purpose of this lab is to make a simple instrument,
to learn how to calibrate it and extend its operating range, and to understand
its limitations.
Pre-lab
problems:
PL4.1. A circular current loop of radius a is positioned in the xy plane, centered on the z
axis, Fig. L4.1. Use the Biot-Savart law to find the expression for the magnetic flux density
vector along the z axis.
r
SIMPLE ELECTROMAGNETICS
272
LABS
PL4.2. Find the magnetic force that acts on a small current element positioned on the z axis
in the yz plane, making an angle of 45° with the z-axis (Fig. L4.l).
Lab:
Equipment and parts:
-
a dc power supply; a multimeter;
-
a compass,
insulated
wire, two potentiometers.
z
Fig. L4.1. A circular current loop in the xy plane and a current element on the axis of the current
loop.
Part
1: Calibrating
the ammeter
You can make an ammeter by winding insulated wire (about 30-40 turns) around a compass.
Connect the ammeter as shown in Fig. L4.2a. The pot resistor is used in series with the power
supply and ammeter in order to limit the current. Set it to 50 n. You can measure the current
either by inserting a commercial ammeter in series in the circuit, or by measuring the voltage
across the pot.
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Power
supply
(a)
Fig. L4.2.
ammeter.
(a) Setup for calibrating the ammeter.
(b) Setup for increasing the current range of the
LAB
273
4: MAGNETIC FIELD AND CURRENTS: AN AMMETER
L4.1. Start with a low voltage (about 1 V) on the power supply, and slowly increase it. You
should see the compass needle deflect as you increase the current through the solenoid up to a
certain point. How do you orient the compass initially so that you measure the largest current
range?
L4.2. In order to be able to use your ammeter, you need a scale. Draw the scale on a piece of
paper by measuring known currents (this is what the commercial ammeter is for) and recording
the compass needle deflection. What is the largest value of the current you can measure? What
is the smallest nonzero current you can measureZ What is the sensitivity of your ammeter,
i.e., how accurately can you measure small changes? Is your scale linear (it is linear if the"
deflection angle is linearly proportional to the current with some multiplication constant)?
.
L4.3. Compare your scale with that of your classmates. How do they compare? How practical
is your ammeter for manufacturing?
..Part
2:
Measurement
of the earth's
magnetic field
The earth is a large magnet and the initial position of the needle is determined by the earth's
-magnetic field. (You can read more about this in Chapter 17 in Introductory Electromagnetics.)
L4.4. Determine the position of the compass that would allow you to have the needle deflect
a known amount when the magnetic field generated by the current is equal to the earths'
magnetic field. Measure the required current for this case.
L4.5. From the value of current obtained in L4.4 and your prelab homework PL4.1 results,
determine the magnetic flux density that the needle is in. This is the value of the earth's
magnetic flux density at the place where the needle is located. What approximations do you
have to make when answering this question?
Part
3: Measuring
larger
currents
(changing
the current
range)
L4.6. You have found that after the current is increased beyond a certain point, there is no
further deflection of the needle (your instrument is saturated). Also, after some current level,
you will burn the resistor that regulates the current. The setup shown in Fig. L4.2b can be
used to measure
larger currents.
Explain
how it works.
Find the current
h
as a function
of
the resistor values Rl and R2.
L4. 7. Determine the values of Rl and R2 that allow you to measure a current range 3 times
larger than the one you had in Part 1. Set the values of the pots to those you calculated and
calibrate a new scale. What is the smallest nonzero current you can measure? What is the
sensitivity of your ammeter?
Conclusions:
1. A current produces a magnetic field. By measuring the torque of this field on a small
magnet, we can measure the current.
2. Every instrument needs to be calibrated.
of the instrument.
The calibration is different for different ranges
3. The simple ammeter you made can be used to indirectly measure the intensity of the
magnetic field of the earth at the place where the ammeter is located.