Resistance

What is resistance?

The electrical resistance of an object is a measure of its opposition to the passage of an electric current.

It is a property of the material that restricts the movement of free electrons in the material.It determines the size of the electric current passing through the material.


Measuring Resistance



The resistance R of a component is defined as the ratio of the potential difference V across it to the current I flowing through it.



Where,

R - resistance,
I - current flowing through the circuit,
V - p.d. across component

The SI unit for resistance is Ohm ().


Measuring resistance

An instrument for measuring resistance is called an ohmmeter. Simple ohmmeters cannot measure low resistances accurately because the resistance of their measuring leads causes a voltage drop that interferes with the measurement, so more accurate devices use four-terminal sensing.


Ohm's Law

The relationship between voltage*, resistance* and current* is expressed in Ohm's Law which is named after the physicist who discovered it.

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them.

Ohm's Law most simply translates to the equation,

V = IR,

Voltage = Current × Resistance

or



where,

I - current through the resistance in amperes,A.
V - potential difference measured across the resistance in volts,V.
R - resistance of the conductor in units of ohms,Ω.

More specifically, Ohm's law states that the R in this relation is constant, independent of the current

If the resistance of a component is constant (stays the same) for different values of V and I, then a plot (graph) of V against I will be a straight line.
The gradient (slope) of the line shows how big the resistance is.



This is all, however, when all physical conditions are constant (e.g. at constant temperature).

Worked Example

Bicycles with battery operated lights often have different size bulbs for the front and rear lights. The filament in the front lamp has a resistance of 3 ohms. It takes a current of 0.6A. What voltage does it work at?

1. 0.2V
2. 1.5V
3. 1.8V
4. 5V

Answer

The answer is 1.8V. If you didn't get the correct answer, have another look at the formula before you try again.


Series circuits

When components are connected in series, their total resistance is the sum of their individual resistances. For example, if a 2Ω resistor, a 1Ω resistor and a 3Ω resistor are connected side by side, their total resistance is 2 + 1 + 3 = 6Ω.


Sum of resistance is 6 ohms

If you increase the number of lamps in a series circuit, the total resistance will increase and less current will flow.


Variable resistors

The resistance in a circuit can also be changed using variable resistors. For example, these components may be used in dimmer switches, or to control the volume of a CD player.


The filament lamp

You should be able to recognise the graph of current against voltage for a filament lamp.


Background

a circle with a diagonal cross through the middle.




Filament lamp symbol

The filament lamp is a common type of light bulb. It contains a thin coil of wire called the filament. This heats up when an electric current passes through it and produces light as a result.

Ohm's Law revisited

graph showing current on the y axis and voltage on the x axis. A line is drawn through the centre of the graph at 45 degrees.


Relationship between current and voltage when a resistor follows Ohm's Law

Remember that the current flowing through a resistor at a constant temperature is directly proportional to the voltage across the resistor. The graph shows what happens to the current and voltage when a resistor follows Ohm's Law.


The filament lamp

The filament lamp does not follow Ohm's Law. The resistance of a filament lamp increases as the temperature of its filament increases. As a result, the current flowing through a filament lamp is not directly proportional to the voltage across it. This is the graph of current against voltage for a filament lamp.


Relationship between current and voltage for a filament lamp

The thermistor

Thermistors are used as temperature sensors, for example, in fire alarms. Their resistance decreases as the temperature increases:


Thermistor symbol

* At low temperatures, the resistance of a thermistor is high, and little current can flow through them.
* At high temperatures, the resistance of a thermistor is low, and more current can flow through them.

Current Electricity

Electric Current

Electric current is the rate of charge flow(of electrons from negaticely charged end to a positively charged end), measured in Coulombs/second which is named Amperes.


Conventional current and electric flow



An electron flow is the movement of electrons towards the positively charged end.

While,

Conventional current flow is the assumption of scientists that an electric current consisted of positive charges flowing from a positively charged end to a negatively charged end.



(Imaginary positive particles moving in the direction of the conventional current).


How is electric current measured?

Since electric current involves moving electric charges, it can be measured by determining the amount of electric charge that passes through a conductor.

Current is the rate at which charge flows past a point on a circuit. As depicted in the diagram below, the current in a circuit can be determined if the quantity of charge Q passing through a cross section of a wire in a time t can be measured. The current is simply the ratio of the quantity of charge and time.



Current is a rate quantity.



Note that the equation above uses the symbol I to represent the quantity current.

The S.I. unit for current is the ampere. Ampere is often shortened to Amp and is abbreviated by the unit symbol A. A current of 1 ampere means that there is 1 coulomb of charge passing through a cross section of a wire every 1 second.

1 ampere = 1 coulomb / 1 second

Electric current is measured using an ammeter.
The ammeter must be connected in series in an electric circuit.

Electric Circuit symbols

A basic closed electrical circuit is made of four basic parts.

1. Electrical Energy Source : The energy source that drives the electric charge round the circuit

2. Electrical conductors or wires : Conductors are used to connect the components together.

3. Electrical load : This enables moving charges to do a useful job. Examples include this computer or even an electric bulb

4. Electrical switch : This enables the users to open and close the circuit.

An open circuit occurs when there is a break in the circuit to stop the current from
flowing.


Electromotive force

In an electric circuit, electromotive force is the work done by a source in driving a unit charge round a complete circuit.

It is more commonly referred to by the initials EMF. EMF is another term for electrical potential, or the difference in charge across a battery or voltage source.

In symbols:

ε = W/Q

where ,

ε - e.m.f. of the power supply,
W - Amount of electrical energy converted from non-electrical forms (work done)
Q - Amount of Charge


The S.I. unit of e.m.f. is joules per coulomb ( J/C) or Volt (V)

How do we measure e.m.f.?

To measure e.m.f, we use a volmeter connected in parellel to the circuit.


What is potential difference?

The potential difference (p.d.) between two points in an electric circuit is defined as the amount of electrical energy converted to other forms of energy when one coulomb of positive charge passes between the two points.

In Symbols:

V = W/Q

where,

V is the potential difference,
W is the electrical energy converted to other forms,
Q is the amount of Charge

The SI unit for the potential difference is the same as that for e.m.f., Volt(V).