Chapter Four

Current, Resistance and Resistivity

1. Current A current is any motion of charge from one region to another, or

The electric current is defined the rate of charges flowing across any

cross-sectional area per unit time, The symbol of current is (I).

Mathematically we can write current as;

Where q is the amount of charges passing through a cross section area per time t.

In SI system, the unit of current is Ampere or (A)

1 Ampere = 1 C/s

In an ordinary metal such as Cu or Al, some of the electrons are free to move at

room temperature.

The electrons do not escape from the conducting material, because they are

attracted to the positive ions of the material.2

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A metal conductor distributes its free charges randomly where it is not

under any external force.

When the metal is connected to a source of a voltage, the free charges will

align themselves into a certain direction under the effect the electric field.

Current I drives itself opposite to the direction of free electrons through

out the circuit.

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Burn that in mind, in metals, the only charges which responsible

of connection are free electrons (negative charges).

However, in semiconducting materials, such as a doped Silicon, both

holes (positive charges) and electrons (negative charges) are

responsible of connecting electricity.

2. A Simple Way To Produce Current By forming Positive And

Negative Charges

Part of the electric circuit that includes this light bulb passes through a beaker with a solution of

sodium chloride. The current in the solution is carried by both positive charges ions and negative

charges (Cl- ions). (Na+)5

3. Some methods to generate current (electricity)

Solar cells

Wind

Power

Electric

generator 6

4. Types of current

There are two types of electric current: Direct current

(DC) and Alternating current (AC).

In DC, The electrons flow in one direction continuously. An example

of DC is the current produced by a battery.

In AC, The electrons flow in two different directions (fist forward

and then backward). An example of AC is the current produced by

the electric generator.

We can plot the AC and DC graphs as below:

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5. Sources of DC and AC

DC sources such as: solar cells, batteries and capacitors.

AC source such as: electric generator.

Most of the devices accept AC as the main current entrance.

However, the apertures inside them such as capacitors work with DC.

As a result, current must be converted into DC inside the devices.

Some other devices accept AC and DC at the same time, for example,

radio and TV.

Some other devices accept AC only and they work under that type of

current. examples are refrigerators and air-conditions.

For a source like solar cells, an invertors is needed to invert the DC

to AC, then transfer the current to the division centres.

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6. Electric resistance and ohm’s law

The German scientist Georg Ohm was the first one discovered that

there is a linear relationship between Current and Voltage.

Ohm’s law states that the current I passing through a material

connected to an energy source V is given by the equation;

I = V/R.

R is the constant of proportionality and is called

electrical resistance.

The unit of resistance is OHM (Ω).

A material with a very large value of R will pass almost no current

(electrical insulator), while another material with very small R will

yield a large current for the same voltage (good electrical conductor).

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Resistor: is a device used in electronic circuit aimed to protect some

other elements from collapse. It can perform that via controlling the

current passing through elements.

This ability is called resistance.

Resistors can come in different

types and shapes.

The symbols of resistors are;

Resistance is the degree of opposition to the flow of electrons in a

material.

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Ohm’s law curves

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7. Resistivity

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As It was mentioned, the relation between current and voltage changes with a proportion called resistance. Now we have to see how resistance changes as a function of the length and the area of the material where current passes though it.

Resistance can be compared to a traffic jam. More car makes the way harder to drive, and visa-versa is true.

For a longer metal conductor, the incoming charges will face a higher columbic force due to facing more charge carriers which they appose the movable charges to drive into a certain direction at the same time.

This means that resistance (R) proportion directly with the metal length (l)

This is, however, for wider road, easer to drive. Means that resistance proportion inversely with the Area (A) passing through it.

We can connect these three parameters (R), (L) and (A) in one formula called resistivity.

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Note: the unite of resistivity is ohm.meter (Ωm).

Or we can say ….. (eq1)

HW:

From the equation 1 above, prove that the unit of resistance (R) is Ω.

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Resistivity of some materials:

HW: we are saying that the resistivity of any

material is constant as it is seen in this table,

Therefore, we also said that resistivity depending

on Both the length and the area of the material.

Don’t you thing the resistivity changes if we

increase the length (only) of a conductor?

Example 1

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Example 2

8. Connecting resistors in series

The two resistors R1 and R2 can be connected in series to a voltage source ΔV. By current conservation, the same current I is flowing through each resistors.

The total voltage drop from a to c across both elements is the sum of the voltage drops across the individual resistors:

The two resistors in series can be replaced by one equivalent resistor Req .

The total (equivalent) resistance of the circuit is larger than the each of the resistors at the circuit. 16

9. Connecting resistors in parallel

let’s consider two resistors R1 and R2 that are connected in parallel

across a voltage source.

By current conversion, the current I that passes through the voltage

source must be divided into a current I1 that passes through resistor

R1 and current I2 that passes through resistor R2.

Each resistor individually satisfies ohm’s law:

And

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10. Internal Resistance

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The potential difference across a real source in a circuit is not equal to

the emf. The reason is that where charges moving through a material of

any real source encounters resistance. We call this the internal resistance

of the source, denoted by (r).

If this resistance behaves according to Ohm’s law, r is constant and

independent of the current I. As the current moves through, it

experiences an associated drop in potential equal to Ir.

Thus, when a current is flowing through a source from the negative

terminal (b) to the positive terminal (a), the potential difference

between the terminals is:

11. Work done by electric current and its power

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For a circuit connected with a battery, charges need to be transferred

from one terminal of the battery to another. For that purpose, the

work is required which is:

Power: the electric energy decapitated in a resistor per unit time is

called the power dissipated by the resistor. Here there power

dissipated by the resistor is giving by:

The unit of power is watt (W).

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Power requirement of some household appliance.

Example 3

Solve:

Symbols for Circuit Diagrams

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Electric Circuits

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