20.1 Electromotive force
Voltage (PD and EMF)
In the circuit below, several cells have been linked in a line to form a battery. The potential difference
(PD) across the battery terminals is 12 volts (V). This means that each coulomb (C) of charge will ‘spend’
12 joules of energy in moving round the circuit from one terminal to the other.
The PD across the bulb is also 12 V. This means that, for each coulomb pushed through it, 12 J of
electrical energy is changed into other forms (heat and light energy).
PD may be measured using a voltmeter as shown above.
PD, energy, and charge are linked by this equation:
energy transformed = charge x PD
For example, if a charge of 2 C moves through a PD of 3 V, the energy transformed is 6 J.
The voltage produced by the chemical reactions inside a battery is called theelectromotive force (EMF).
When a battery is supplying current, some energy is wasted inside it, which reduces the PD across its
terminals. For example, when a torch battery of EMF 3.0 V is supplying current, the PD across its
terminals be might be only 2.5 V.
20.2 Internal resistance of sources
Internal resistance
. In reality, when a battery is supplying current, its output PD is less than its EMF. The greater the current,
the lower the output PD. This reduced voltage is due to energy dissipation in the battery. In effect, the
battery has internal resistance. Mathematically, this can be treated as an additional resistor in the circuit.
The battery above is supplying a current 1 to an external circuit. The battery has a constant internal
resistance r. From Kirchhoffs second law E= IR+ lr
But V= IR, so E= V+ lr
So V= E- Ir ……………(1)
The graph above shows how V varies with I. Unlike earlier graphs, V is on the vertical axis.
Note:
• When I is zero, V = E. In other words, when a battery is in open circuit (no external circuit), the PD
across its terminals is equal to its EMF
• When R is zero, V is zero. In other words, when the battery is in short circuit (its terminals directly
connected), its output PD is zero. In this situation, the battery is delivering the maximum possible current,
lmax, which is equal to E/r. Also, the battery’s entire energy output is being wasted internally as heat.
• As Imax = E/r, it follows that r = E/lmax. So the gradient of the graph is numerically equal to the internal
resistance of the battery.
If both sides of equation (1) are multiplied by I, the result is Vl = El- I2r. Rearranged, this gives the
following:
Contoh 1
Sel kering dengan EMF/dge 1.5 V disambungkan secara sesiri dengan perintang dan bateri. Jika arus
3.0 A mengalir, voltan/PD merentasi sel adalah 0.42 V. Apakah rintangan dalam sel kering?
20.3 Kirchhoff’s law
Kirchhoff’s first law
The currents at junctions X and Y above illustrate a law which applies to all circuits:
TotaI current out of junction = total current into junction
This is known as Kirchhoff’s first law. It arises because, in a complete circuit, charge is never gained or
lost. It is conserved. So the total rate of flow of charge is constant.
Let’s consider :
Current Junction:
Arah positif : I1,I2
Arah negatif: -I3,-I4,-I5
Maka menggunakan hukum Kirchoff : SI = I1 + I2 +( -I3) + (-I4) + (-I5) = 0
Resistors in series
If R1 and R2 below have a total resistance of R then R is the single resistance which could replace them.
From Kirchhoff’s first law, all parts of the circuit have the same current /through them.becouse there is
only one input and one output
From Kirchhoff’s second law E= IR and E= IR1 + IR2.
So IR = IR1 + IR2
\ R=R1+R2
For example, if R1 = 3 W and R2 = 6 W, then R = 9 W.
Kirchhoff’s second law
The arrangement above is called ‘a circuit’. But, really, there are two complete circuits through the
battery. To avoid confusion, these will be called loops.
In the circuit above, charge leaves the battery with electrical potential energy. As the charge flows round
a loop, its energy is ‘spent’ – in stages – as heat. The principle that the total energy supplied is equal to
the total energy spent is expressed by Kirchhoff’s second law.
Round any closed loop of a circuit, the algebraic sum of the EMFs is equal to the algebraic sum of
the PDs (i.e. the algebraic sum of all the IRs).
Note:
•From the law, it follows that if sections of a circuit are in parallel, they have the same PD across them.
•’Algebraic’ implies that the direction of the voltage must be considered. For example, in the circuit below,
the EMF of the right-hand battery is taken as negative (-4 V) because it is opposing the current Therefore:
algebraic sum of EMFs = 18 + (-4) = +14V
algebraic sum of IRs = (2 x 3W) + (2 x 4W) = +14 V
Lets consider:
Closed Loops
Paralell
Series
Resistors in parallel
From Kirchhoff’s second law (applied to the various loops):
E = IR (Loop with total Resistor)
and
E = I1 R1 (Loop with Resistor R1)
and
E = I2 R2 (Loop with Resistor R2)
From Kirchhoff’s first law I = I1 + I2.
So
Kegunaan hukum Kirchoff di dalam litar adalah untuk menentukan nilai arus dan arah arus pada satusatu litar:
Contoh 2
Didalam litar di bawah, dge bateri E1 ialah 21V dan rintangan dalamnya diabaikan dan EMF bateri
E2 ialah 84V dan rintangan dalamnya ialah r2 = 4W.
Contoh 3
Calculate the current I, the resistance R and the e.m.f. E for the circuit below.
20.4 Potential divider
Potential divider
A potential divideror potentiometer like the one below passes on a fraction of the PD supplied to it.
In the input loop above, the total resistance = R1 + R2.
So
But Vout = IR2,
so
Note:
•The above analysis assumes that no external circuit is connected across R2. If such a circuit is
connected, then the output PD is reduced.
In electronics, a potential divider can change the signals from a sensor (such as a heat or Iight.detector)
into voltage changes which can be processed electrically. For example, if R2 is a thermistor, then a rise in
temperature will cause a fall in R2 and therefore a fall in Vout. Similarly, if R2 is a lightdependent resistor
(LDR), then a rise in light level will cause a fall in R2, and therefore a fall in Vout.
Potential dividers are not really suitable for high-power applications because of energy dissipation
20.5 Potentiometer
(a) The idea of potentiometer
Function : To measure emf a cell
Key Idea : make sure the galvanometer as a null detector
E = lV
where
V = potential difference per unit length of AB.
L = The length of wire
l = length that galvanometer show zero reading
so PD across l,
Potentiometer Applications
(a) Measuring a cell’s internal resistance.
or
If a graph is plotted,
Gradient,
Internal resistance,
Intercept,
(b) Comparing resistance
20.6 Wheatstone bridge
6 Wheatstone Bridge
20.7 Shunt and multiplier
9 Shunts and Multipliers
(a) Conversion of milliammeter to ammeter
Since
(b) Conversion of milliammeter to voltmeter