EMF (previously known as "electromotive force")
If a charged particle, such as an electron, moves through an electric
field, there will be a conversion between electric potential energy and
kinetic energy. The energy is originally provided to the charge by a
chemical reaction or an electromagnetic effect. EMF is not actually a
force, but a measure of how much energy is provided to each coulomb of
charge. i.e. a voltage.
However, EMF measures the total work done by the source, before any is
lost, say through internal resistance. Any source, such as a cell or
generator has internal resistance, so it is not possible simply to measure
the voltage at the output to determine the EMF, but we can come close.
The voltmeter measures the
voltage across the circuit
resistance, which is equal to the
EMF minus the voltage drop across
the internal resistance of the cell.
If a voltmeter is connected directly to the terminals of the power source,
we can measure the "open circuit terminal voltage".
The resistance of a voltmeter is typically
20 000 Ω per volt. The internal resistence
of the source may only be a few Ω.
Therefore the voltage drop across the internal resistance is insignificant
compared with the voltmeter's own internal resistance, so the measured
voltage is very close to the EMF.
Problem:
A cell has an EMF of 1.5V. When it is new the internal resistance is 0.5Ω,
but with age and use it rises to 100Ω.
Find the open circuit terminal voltage that will be measured by a voltmeter
with an internal resistance of 10kΩ in each case.
If an ammeter with negligible internal resistance is connected directly
across the terminals of the cell, what will the current measurement be for
a new and an old cell?
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Resistors in Series and Parallel
Kirchhoff's Current Law
At any point or junction in a circuit, the total current entering is equal to
the total current leaving.
Kirchhoff's Voltage Law
Around any complete loop in a circuit, the total of the energy gains is equal
to the total of the energy losses, i.e. total voltage change = 0.
Resistors in Series
I, V are the total current and voltage
The voltage across each resistor is V1,
V2, V3 etc.
The current through each resistor is
I1, I2, I3 etc.
V = IR
V1 = I1R1, V2 = I2R2, V3 = I3R3
V = V1 + V2 + V3 ......
IR = I1R1 + I2R2 + I3R3...
but I = I1 = I2 = I3 ...
so IR = IR1 + IR2 + IR3 ...
R = R1 + R2 + R3 ...
Resistors in Parallel
I = V/R
I1 = V1/R1, I2 = V2/R2, I3 = V3/R3
I = I1 + I2 + I3 ....
V/R = V1/R1 + V2/R2 + V3/R3
but V1 = V2 = V3 ....
so V/R = V/R1 + V/R2 + V/R3
I, V are the total current and
voltage.
The voltage across each
resistor is V1, V2, V3 etc.
The current through each
resistor is I1, I2, I3 etc.
1/R = 1/R1 + 1/R2 + 1/R3 ....
Caution:
After you have calculated 1/R,
do not forget to calculate and
state the total resistance R.
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Use and Placement of Ammeters and Voltmeters
An ammeter is intended to measure the current at a point in a circuit. It
has a very low internal resistance, so that it will use a small sample of the
energy from each electron that passes that point. It must be connected
in series with the other circuit components.
A voltmeter is intended to measure the energy difference across a
component or part of a circuit. It has a very high internal resistence, so
that it will use all the energy from a small sample of the electrons that
would otherwise pass through the circuit. It must be connected in parallel
with the other circuit components.
If the ammeter is connected in parallel, its
very low resistance means that a high current
will flow through it, because the total
resistance of the circuit is very low. The
ammeter will probably be damaged.
If the voltmeter is connected in series, its high
resistance means that the current in the circuit
will be very low - the circuit will "not work":
The Potential Divider
Suppose two resistors are connected in series across a power supply, with
potential difference V. If the negative terminal is defined as potential 0,
then the point between the two resistors will be at a potential somewhere
between 0 and V, depending on the ratio of the two resistances. This
arrangement is known as a potential divider, as the potential of the power
supply is divided into two parts.
If a circuit is connected to the 0 potential and the central point, then any
P.D. between 0 and V can be applied to that circuit, which is not possible
with the use of a simple series or parallel resistor in the circuit.
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Applications
1. Voltage Adjustment
The two resistors can, in fact, be a single coil of resistance wire, with
connections at both ends and a movable "tap" connecting to some point in
between. This device is known as a "potentiometer". This is used, for
example, in the volume control of a sound system, prior to the final
stages of signal amplification.
2. Sensors
One resistor may have a fixed value and the other may vary in response
to some environmental influence. A voltmeter can then be calibrated
directly to measure the environmental factor.
e.g. A light dependent resistor (LDR) makes a light-meter. A thermistor
makes an electronic thermometer (NTC = "negative temperature
coefficient thermistor - resistance decreases as temperature increases).
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