Ohm's law, resistance and resistivity

 OHM’S LAW

Before going to Ohm’s law let us discuss in brief about some electrical components or devices we use in electric circuits.

  

A Battery serves as a source of electricity in a circuit.

We use mainly two measuring devices in this concept those are 

Volt meter: used to measure potential difference between the two ends of a conductor. So it is always connected in parallel ( we learn about types of connections later in this chapter)

Ammeter: used to measure the current passing in the circuit. So it is always connected in series.

Now let us dive in to the activity did by Ohm to understand his concept.

Materials required: 5 dry cells of 1.5V each, conducting wires, an

ammeter, a volt meter, thin iron spoke of length 10cm, LED and key.

 

Procedure: Connect a circuit as shown in the above figure.

Solder the conducting wires to the ends of the iron spoke. Close the key. Note the readings of current from ammeter and potential difference from volt meter in table

 

  Now connect two cells (in series) instead of one cell in the circuit.

Note the respective readings of the ammeter and volt meter and record the values in table. Repeat the same for three cells, four cells and five cells respectively. Record the values of potential difference (V) and current (I) corresponding to each case in the table 1. Find V/I for each set of values.

What do you notice? The ratio V/I is a constant. We can write this mathematically as V ∞ I

From this experiment we can conclude that the potential difference between the ends of the iron spoke (conductor) is directly proportional to the current passing through it (assuming the temperature of the iron spoke is constant during the flow of current through it).

  Draw a graph between V and I taking the current (I) along y-axis and potential difference (V) along x-axis with appropriate scale. 

 

You will get a straight line graph passing through the Origin.

Now try to repeat the activity with any semiconductor like L.E.D, then plot a graph. The long terminal of the LED is connected to the positive terminal of the battery and short terminal of the LED is connected to negative terminal of the battery.

 

Draw a graph between V and I for LED. You will get a curved graph.

So, we can conclude that the ratio between V and I is constant for some materials at constant temperature. This fact was established by German Physicist, George Simon Ohm and it is popularly known as Ohm’s law.

We can define Ohm’s law as follows.

“The potential difference between the ends of a conductor is directly proportional to the electric current passing through it at constant temperature”.

Let V be the potential difference between the ends of the conductor and I be the current passing through it.

V ∞ I    (temperature is constant)

V/I = Constant

This constant is called resistance of the conductor. It is denoted by

‘R’. Then we get V/I = R.

V = IR  [ohm’s law formula]

The SI unit of resistance is ohm. The symbol of ohm is Ω.

1 Ohm = 1 Volt/1 Ampere

1 Ω = 1V/A (volt/ampere)

Based on Ohm’s law materials are classified into two categories. Those which obey Ohm’s law are called ohmic materials. For example, metals are ohmic materials. Those which do not obey Ohm’s law are called non ohmic materials. For example, LEDs are non ohmic materials.

The resistance of a conductor is defined as the obstruction to the motion of the electrons in a conductor. 

The material which offers resistance to the motion of electrons is called resistor.

FACTORS AFFECTING RESISTANCE:

It is very important to analyse that, on what factors a resistance of a conductor depends upon.

Resistance depends upon four factors

1) Temperature

2) Nature of the material

3) Length of the conductor

4) Area of cross section of the conductor.

The first two factors are not physically seen. 

Depending upon nature of the substance resistance varies from body to body.

Resistance is directly proportional to temperature.  As temperature increases resistance increases and vice versa.

Now, coming to the last two factors they can be seen physically. 

 

Resistance is directly proportional to length of the conductor at constant temperature and constant area of cross section.

R ∞ l ..................(1) (at constant temperature and cross sectional area)

The resistance of a conductor is inversely proportional to its cross section area.

R ∞ 1/A  .................. (2) (at constant temperature and length of the conductor)

From the equations (1) and (2), we get

R ∞l/A (at constant temperature)

R = ρl/A

Where, ρ (Rho) is a proportionality constant and it is called specific resistance or resistivity.

The SI unit of resistivity is Ω - m.

The reciprocal of resistivity is called conductivity (σ).