Electrical Measurements
Ohm’s law states that for most substances the current (I) the through the material is proportional to the
potential difference (V) across the material. The proportionality constant is the resistance (R). That is
V = IR
(l)
Devices that obey Ohm’s law are called linear devices. Devices that do not obey Ohm’s law are called
nonlinear devices. The units of V are volts, the units of I are amperes, and the units of R are ohms.
A galvanometer is a device whose deflection of the needle is proportional to the current going through the
meter. The galvanometer is then described by the amount of current required to give full scale (IG) and the
internal resistance (r).
A voltmeter consists of a fixed resister R in series with the galvanometer (Fig. 1). Using ohm’s law, the
reading on the galvanometer can be shown to be proportional to voltage. (Eqn (2)). Once the characteristics
IG and r of the galvanometer are known. Then R can be calculated for a particular full scale deflection of V.
V = IG (R+r) (1)
Fig. 1 A galvanometer can be used in the construction of a multi-meter that has several ranges of voltages by
replacing R with the appropriate value. A voltmeter can be used to measure the voltage of an element by
placing it in parallel with the element.
An ammeter consists of a shunt resistor (S) in parallel with a galvanometer (Fig. (2)). The total current I
divides and part goes through the shunt (IS) and the rest goes through the galvanometer
(IG). The current IG is proportional to the total current I (Eqn (3)).
Using Ohm’s law IS = V/S, IG = V/r and I = IG + IS
and I = ((r+S)/S) IG (2)
If r and IG are known, then S can be found for a
particular value of I.
Fig. 2 Apparatus:
1.
Galvanometer
2.
Multimeter
3.
Two Resistance boxes
4.
Wires
5.
Coil of wire of known resistance per unit length
Procedure:
1. Hook up the circuit in Figure 3 and adjust the resistance R such that the galvanometer gives full-scale
deflection. Record the voltage of the power supply and the resistance R. Keeping the voltage V and
the resistance R unchanged, now hook a second resistance S in parallel with the galvanometer as
shown in Figure 4. Adjust S so that the current reads 1/2 of full scale. The internal resistance of the
galvanometer is equal to S and full scale deflection IG can be calculated from Equation 2.
Fig. 3 Fig. 4 2.
Using Eqn 2, calculate the value of R such that full scale deflection is 5 volts. Show work on the
back of the sheet. Using the multimeter as a voltmeter set the voltage output of the power supply to 3
volt. Now measure the same voltage with the voltmeter just constructed out of the galvanometer. The
circuit will bethe same as Figure 3.
3.
Repeat the above for a full-scale deflection of 50 volts. Set the power supply to 20 Volts to check your
answer.
4.
Using Equation (3), calculate the value of S for a full-scale deflection of 5 mA. Show your work on
the back of the sheet. Construct the shunt resistance out of a resistance box plus a length of wire such
that the value of the shunt is within 0.1 ohms of its calculated value. Using the multi-meter as an
ammeter, hook it in series with a resistance box, galvanometer, and power supply as shown in Figure
5. Adjust the power supply so that the multi-meter reads 3 mA. Compare with the galvanometer
reading.
Fig. 5 5.
Repeat the procedure above for 50 mA full scale deflection. Set the multimeter to 30 mA to check
your calculations.
Data:
1.
Measurement of Characteristics of the Galvanometer
V = _________________
R = _________________
S = __________________
IG = ________________ (Eqn 2)
2. Construction of a Voltmeter (Full scale deflection of 5V)
R = ____________________ (Eqn 2)
V(galvanometer) = ___________ V(multimeter) = __________
percent error = ________________
3.
Construction of a Voltmeter (Full scale deflection of 50 V)
R = ____________________ (Eqn 2)
V(galvanometer) = ___________ V(multimeter) = __________
percent error = ________________
4. Construction of an Ammeter (Full scale deflection of 5 mA)
S = _________________ (Eqn 3)
I(galvanometer) = _____________ I(multimeter) = __________
percent error = ______________
5.
Construction of an Ammeter (Full scale deflection of 50 mA)
S = _________________ (Eqn 3)
I(galvanometer) = _____________ I(multimeter) = __________
percent error = ______________