Download Electric Circuit

Electric Circuit
(A) Electric current
An electric current is the rate of flow of charge in a circuit.
charge
Q
, i.e. I 
time
t
Current is measured in ampere (A) by an ammeter.
Current =
In a simple circuit, the current through every part is the same. The conventional current goes
round the circuit from the positive terminal of the battery to the negative terminal. It is opposite
to the flow of electrons.
(B) Electrical energy and voltage
The voltage across two points is the electrical energy transferred per coulomb of charge
passing through the points.
Voltage 
electrical energy
E
, i.e. V 
charge
Q
Voltage is measured in volts (V) by a voltmeter or a voltage sensor. 1 V = 1 J C-1
In a simple circuit, the voltages across each device add up to a sum equal to the voltage of the
battery.
The voltage across devices connected in parallel is the same.
The total voltage of cells is equal to the sum of the voltage of all the cells if they are in series;
and the voltage of a single cell if in parallel.
(C) Resistance
(1) What is resistance?
Resistance is the opposition of a conductor to current.
Resistance 
voltage across conductor
V
, i.e. R 
current through conductor
I
Resistance is measured in ohm (Ω). 1Ω=1VA-1
Electric Circuit
1
(2) Ohm’s Law
A metallic wire (e.g. eureka wire) is connected to a battery and a rheostat as shown in the
following figure.
By adjusting the rheostat, a graph of the voltage across the eureka wire against the current
flowing through it is then plotted. From the graph, it shows that the voltage across the eureka
wire is directly proportional to the current flowing through it. The Ohm’s Law is then verified.
Ohm's law states that the voltage across the ends of a metallic conductor is directly proportional
to the current flowing through it, provided the temperature and other physical conditions are
unchanged. In other words, the resistance of a metallic conductor is a constant, provided the
temperature and other physical conditions are unchanged.
Not all conductors obey Ohm's law. The resistance of a conductor that obeys the Ohm’s Law is
equal to the slope of the voltage-current graph.
Voltage-current graph of conductors obeying Ohm’s Law
Electric Circuit
Voltage-current graph of conductors NOT obeying Ohm’s Law
2
(3) Factors affecting resistance
The resistance of most metals increases with temperature.
The resistance R of a metal wire depends on
(a) its length  ,
(b) its cross-sectional area A, and
(c) the material from which it is made.
The resistance of a conductor of the same material is related to its length  and
cross-sectional area A as shown in the following: R 

A
(4) Measuring resistance
The resistance of a conductor can be measured using the voltmeter-ammeter method. Then,
the resistance is given by the following.
Resistance 
voltmeter reading
ammeter reading
(5) Combination of resistors
A resistor is a device with known resistance. Fixed resistors have fixed values of resistance
while variable resistors, such as rheostats, have variable resistance.
Resistors in series and in parallel
Resistors in series: R  R1  R2  R3  ...
Resistors in parallel:
Electric Circuit
1
1
1
1



 ...
R R1 R2 R3
3
(6) Short circuit
A resistor is short-circuited if a wire is connected across it. The wire has almost zero resistance
and so most of the current passes through it rather than the resistor. Short circuit in the mains
circuit may cause fire.
(7) Ideal ammeter and ideal voltmeter
An ammeter has resistance. The current through the conductor whose current is to be
measured will be lowered with the presence of an ammeter.
Before connecting the ammeter
After connecting the ammeter
In the above circuit, as the total resistance in the circuit is increased after connecting the
ammeter, therefore
the current I’ flowing through R1 after
connecting the ammeter
<
the current I flowing through R1 before
connecting the ammeter
Therefore, an ideal ammeter has a zero resistance.
A voltmeter does not have infinite resistance. The voltage across the conductor whose voltage
is to be measured will be lowered with the presence of voltmeter.
Electric Circuit
4
Before connecting the voltmeter
After connecting the voltmeter
In the above circuit, the equivalent resistance R of the resistor R1 and the voltmeter is smaller
than the resistance of the resistor R1.
Therefore,
Voltage across R1 after connecting the
ammeter
<
Voltage across R1 before connecting the
ammeter
Therefore, an ideal voltmeter has an infinite resistance.
(8) Internal resistance in a cell
A cell in practice has some resistance. This explains the 'lost volt' when the cell is connected to
a circuit.
Electric Circuit
5