Student’s name _____________________________________________________
Experiment E4
DETERMINATION OF EMF BY COMPENSATION METHOD
Objective: to master a method of emf measurement by compensation method.
1 EQUIPMENT
1)
2)
3)
4)
5)
emf sources;
emf standard;
Veston element;
galvanometer;
rheohord, resistances, switches.
2 THEORY AND EXPERIMENTAL SETUP
Every current source redistributes electric charges in an electric circuit. Such redistribution may be caused
by chemical reaction, contact potential, electromagnetic induction, Lorentz force, photoelectric effect, etc.
Forces, produced by all of the noted above phenomena, do nonzero work moving a charge along a closed
path (in distinction from electrostatic field, for which a work along a closed path always equals zero).
These forces are acting in a current source and move charges against electrostatic forces. Chemical sources
of energy are called galvanic elements. If a galvanic battery is used to establish an electric current in a
conductor, there is a continuous transformation of chemical energy in the battery to kinetic energy of the
electrons and then to internal energy in the conductor, resulting in an increase in the temperature of the
conductor. In typical electric circuits, energy is transferred from a source such as a battery, to some device
(called a load or a resistor), such as a lightbulb or a radio receiver. Because the connecting wires also have
resistance, some energy is delivered to the wires and some energy to the resistor. Unless noted otherwise, it
is assumed that the resistance of the wires is so small compared to the resistance of the circuit element that
the energy delivered to the wires may be neglected. Because the potential difference at the galvanic battery
terminals is constant in a particular circuit, the current in the circuit is constant in magnitude and direction
and is called direct current. A battery is called either a source of electromotive force or, more commonly, a
source of emf. (The phrase electromotive force is an unfortunate historical term, describing not a force but
rather a potential difference in volts.) The emf of a battery is the maximum possible voltage that the battery
can provide between its terminals. When an electric potential difference exists between two points, the
source moves charges “uphill” from the lower potential to the higher. Consider the circuit consisting of a
battery connected to a resistor. The positive terminal of the battery is at a higher potential than the negative
terminal. Because a real battery is made of matter, there is resistance to the flow of charge within the
battery. This resistance is called internal resistance r. For an idealized battery with zero internal resistance,
the potential difference across the battery (called its terminal voltage) equals its emf. However, for a real
battery, the terminal voltage is not equal to the emf for a battery in a circuit in which there is a current.
Emf of galvanic element depends only on chemical reaction reaction type and is constant for every
particular type of electrochemical cell
Ohm’s law for a cirquit which contains a emf is written as
(2.1)
ε = IR + Ir ,
1
where ε is value of emf, І is current, R is load resistance, r is internal resistance of emf source. Voltage
across terminals of the source equals voltage on load resistance:
V = IR .
From equation (2.1) it follows that
(2.2)
V = ε − Ir .
Thus the voltage across the load equals emf minus voltage drop on internal resistance of the current
source. In consequence, accurate measuring of ems by voltmeter alone is not possible, because the current
which must flow through the voltmeter to operate it, also flows through the emf source, and voltage drop
on the internal resistance cause the experimental error. Direct use of votlmeter for approximate emf
measurement may be only justified when internal resistance of the voltmeter is very large and thus the
current is very small, then U≈ε.
Compensation method (proposed by J.C. Poggendorf) allows the accurate measurement of emf.
Consider electric circuit shown in figure 2.1:
ε is source with large enough emf value, εХ is the measured
R1
emf, εN is emf standard, G is galvanometer, АВ is calibrated
wire or rheochord.
If emf of the source under investigation εХ has lower
G
εX
rx S
rN
εN
value
than
that of the battery ε, then on the rheochord АВ
+
+
there always is a position C of slide bar, for wich the current
І2
К1
through galvanometer G equals zero. According to
A
B
Kirhhoff’s loop rule for the upper closed loop one may write
І1 D C
the equation
I +
R
− I 2 (rx + R1 + rG ) + I 1 R AC = ε x ,
(2.3)
ε
К
where rx is internal resistance of the source under
investigation, RAC is resistance of АС segment.
If the current through the galvanometer is absent,
Figure 2.1
І2=0, then
I 1 R AC = ε X .
(2.4)
In this case voltage across the segment АС equals the emf of the source under investigation.
If one substitute the source with unknown emf with standard emf source, the position of slide bar
for the absence of current through galvanometer shifts to point D. Then Eq. (2.4) reads as
(2.5)
I 1 R AD = ε N .
Dividing Eq. (2.4) by Eq. (2.5) one has
R
ε X = ε N AC .
(2.6)
R AD
Resistivity of a wire with constant cross-section is given by formula R = ρ
l
, where ρ is
A
resistivity of material, l is length of the wire and A is its cross-section area, so one may simplify formula
(2.6) to have a form
l
εX =εN 1 ,
(2.7)
l2
where l1, l2 are lengths of АС and AD segments, respectively. If εN is known with sufficient accuracy then
measuring АС=l1 and AD=l2, by formula (2.7) one calculate εХ.
In reochord АВ, the wire is fastened to a scale which allows the direct measurement of l1 and l2.
The switch К1 closes the circuit for short period of time (to avoid using up of batteries). The sources εХ or
εN are connected to the circuit in turn, by switch S.
2
+
-
Solution of
CdSO4
Crystals of
CdSO4
Paste
Hg2SO4
Amalgam
HgCd 12,5%
Hg
Figure 2.2
Weston cell, invented by Edward Weston
in 1893, is used in this experiment as standard
emf. The Weston cell is a wet-chemical cell that
produces a highly stable voltage suitable as a
laboratory standard for calibration of voltmeters.
It was adopted as the International Standard for
EMF in 1911. As shown in Figure 2.2, the cell is
set up in an H-shaped glass vessel with the
cadmium amalgam in one leg and the pure
mercury in the other.The anode is an amalgam of
cadmium with mercury, the cathode is of pure
mercury, the electrolyte is a solution of cadmium
sulfate and the depolarizer is a paste of
mercurous sulfate. Electrical connections to the
cadmium amalgam and the mercury are made by
platinum wires fused through the lower ends of
the legs. Weston cell produce wery stable value
of emf, which is almost independent on
temperature. At t=20°С its emf equals 1,0183 В.
The current produced by Weston cell does not
exceed 10-6-10-5 that is why it is used in
compensation circuits and for calibration only.
3 PROCEDURE AND ANALYSIS
3.1 Assemble electric circuit according to diagram shown in Fig. 2.1. Pay attention to batteries polarity.
3.2 Connect the source εХ by switch S.
3.3 Close circuit by switch К, press К1 and set the galvanometer’s pointer to zero, moving slide-bar of the
rheochord.
3.4 Measure length of segment АС= lХ and record this value in the table 3.1.
3.5 Connect the source εN by switch S and perform steps 3.3-3.4 to measure AD=lN.
3.6 Calculate emf value by formula
l
εX =εN X .
lN
3.7 Repeat the measurement for 5 different resistance values of variable resistor R. Fill the table 3.1 with
results of measurements and calculations
Тable 3.1
No
lХ,
mm
lN,
mm
εN,
V
Mean
value
3
εХ,
V
∆εХ,
V
∆εХ/εХ,
%