# Electrical Ohm’s Law

In 1826 famous German scientist Gorge Simon Ohm invented a relation between voltage and current. He expressed the relation in a formula which is known as Ohm’s Law. This formula seems very simple but it has a great contribution in ac current.

**Georg Simon Ohm** (Photo by wikimedia)

Ohm’s Law states “If temperature and physical properties of an element remains same the flow of current through a conductor is proportional to the voltage of the two points of the conductor”.

Mathematical expression of Ohm’s Law Formula:

V∝ I

Potential different between two points means voltage. Potential difference means charge difference of two points. Where quantity of charge differs one point to another charge flows higher to lower point that is called current *I*.

**Figure:** Ohm’s law in simple circuit

A simple circuit shown in figure where E is battery or source, a conductor of R resistance is connected with the battery. Charge difference of the conductor between two points A and B is V = V_{A} – V_{B}

Where V_{A} > V_{B}.

There are no 100% pure materials in the world. Every pure material has an internal resistance of it may the resistance value is very very low but it must has resistance. Hence the conductor is connected with the battery two terminal A point has higher potential or higher charge than B point. From the property of charge we know charge flows higher potential to lower potential so current *I* flows A to B points through R resistance conductor.

According to Ohm’s law at fixed temperature,

*I* ∝ V_{A} – V_{B}

Where V = V_{A} – V_{B}

*I ∝* V

or, *I* = G V ————————— (i)

Here G is a proportional constant. It is known as conductance of conductor.

The equation can be written as V = *I* / G

From the equation it is clear that for a fixed voltage increasing the value of 1/G decreases the value of current *I*. The term 1/G works as prevention of current. For clear conception we take a fixed voltage value 200V, assume value of 1/G = 100

Now I = 200/100 = 2A.

If we increase the value of 1/G = 200 then I = 200/200 = 1A.

That means increasing of 1/G term decreasing the current. So the term 1/G is known as resistance and expressed as R. putting 1/G = R in the equation we get **ohm’s law simplified**

V = *I* R

This is the equation of mathematical form of Ohm’s Law.

**Definition of resistance:** The property of conductor which prevents the flow of charge is called resistance. Current decreases increasing of resistance.

Resistance R is the ratio of voltage V and current I

R = V / I

Cause of resistance of conductor is that when charge electron flows via conductor it gets thrust with atom and other electron which slow down kinetic energy and prevents flow of current. This prevention is called resistance.

**Unit of resistance:** Putting the unit of voltage and current in this equation R = V / I

We get R = Volt / Ampere = V A^{-1}

Unit of resistance is ohm which is written in omega sign Ω.

1 Ω = V A^{-1}

If voltage of a conductor is 1 volt and 1A current flows through the conductor then prevention of the conductor is 1 ohm.

Serial of Ohm value higher to lower

1 Mega-ohm = 1MΩ = 10^{6}Ω

1 kilo-ohm = 1kΩ = 10^{3}Ω

1 milli-ohm = 1mΩ = 10^{-3}Ω

1 micro-ohm = 1µΩ = 10^{-6}Ω

**Conductance: **

From equation (i),

G =I / V

For per unit voltage flow of current via a conductor is called conductance of that conductor.

The value of G those conductors is greater is superconductor and less value of G conductor is insulator.

**Unit:** In equation R = V/I if voltage V is in volt and current I is in Ampere then unit of conductance is mho or Siemens.

**Siemens:** If 1A current passes through a conductor and the voltage of that conductor is 1V then the conductivity of that conductor is 1 mho or 1 Siemens.

1 Siemens = 1 Volt / 1 Ampere

As conductivity is inverse of resistance hence G = 1/R

So that 1S = 1Ω^{-1} = 1 mho

or 1 mho = 1 ohm^{-1}

If resistance of a conductor is 2Ω then conductance of that conductor is

G = 1/R = ½ = 0.5 Ω^{-1}=0.5 S

If cross section area and length of a conductor remain same conductivity of the conductor depends upon temperature and conductor material. Generally all metal are good conductor, its conductivity is high. But conductivity of all metal is not same. For example conductivity of silver than copper and iron is greater. In normal temperature silicon and germanium has low conduction. It is called semiconductor. Increasing of temperature increases of resistance which mean decreasing of conductivity of conductor. But there is exceptionality for silicon or germanium which is semiconductor. For semiconductor temperature rise increases conductivity of it.

**Experimental verification of Ohm’s Law: **

Main theme of Ohm’s law V = IR is that change of voltage V in a circuit changes current I also proportionally. For change of V and I ratio of V/I remains same.

For voltage V_{1} current flow I_{1}, voltage V_{2} current I_{2}, voltage V_{3} current I_{3}

V_{1} / I_{1} = V_{2} / I_{2} = V_{3} / I_{3} = R

For change of voltage current will change according to change of voltage but the ratio will same every time.

Now we will prove that. There are two way to prove that.

**Method 1:** We use a circuit where we change the battery value and note the value current of each battery value.

**Method 2:** We use a fixed voltage battery using variable resistance and changing of resistance we take current and voltage rating each time.

Second method is the best option and easy way to prove Ohm’s law verification.

Apparatus required:

- Battery
- Voltmeter
- Ammeter
- Resistor
- Variable resistor
- Switch

**Figure:** Verification of Ohm’s Law

A battery E is connected with a resistor R in series. Variable resistor Rh also connected in series. K is switch. A voltmeter connected parallelly with resistor two terminal C and D for measuring voltage of resistor. An ammeter connected in series with the circuit for current measurement. Resistor R value is fixed but variable Rh resistor value can be changed. We change the value of Rh then voltage will change and current will change also. We have to note the current value with the voltage reading by changing Rh.

**Process: **

Switch on the circuit. Current flows through the resistor R from C to D point. Ammeter shows the current value I_{1} and voltmeter shows the voltage value V_{1}. Change the variable resistor *Rh* value and find the second current reading I_{2} and voltage V_{2} for it. Again changing value of *Rh* voltage V_{2} and current I_{3} taken.

Suppose we get voltage V_{1}, V_{2}, V_{3} for current I_{1}, I_{2}, I_{3}. Putting the value of voltages in X axis and current in Y axis in a graph we get a straight line.

We are taking three values as assumption

For I_{1} = 2A, V_{1} = 4V

For I_{2} = 3A, V_{2} = 6V

For I_{3} = 4A, V_{3} = 8V

Dividing each voltage with their current get resistance R value.

R_{1} = V_{1 }/ I_{1} = 4/2 = 2Ω

R_{2} = V_{2 }/ I_{2} = 6/3 = 2Ω

R_{3} = V_{3 }/ I_{3} = 8/4 = 2Ω

It is proved that if we increase voltage, current will rise proportionally and the ratio of voltage and current always same in a circuit.

This experiment proves Ohm’s law. That mean V/I is a constant number which is equal to resistance of the conductor R.

**Figure:** Verification of Ohm’s Law in graph

The above graph represents Ohm’s Law. Here we get straight line which marked as red line for three voltages and three currents.

These values are not real we just used to give clear conception.

**Application of Ohm’s law to a simple circuit:**

**Figure:** Ohm’s Law in a simple circuit

The circuit which carries same current on every branch called simple circuit. A simple circuit is shown in figure.

E = Electromotive force

r = internal resistance of the battery

I = total current of the circuit

R = resistance of bulb

V_{1} = voltage of bulb

V_{2} = voltage of battery

We know Ohm’s law, V = IR

Applying Ohm’s law in the simple circuit,

Battery voltage, V_{2} = Ir

It is called lost voltage of battery. Because internal resistance of battery drops it.

Bulb voltage V_{1} = IR

Battery and the bulb are carrying same current I.

E = V_{1} + V_{2}

= IR + Ir

= I ( R+r)

I = E / (R+r)

Total current flow = electromotive force of battery / Total resistance of circuit

It can be said that current of a circuit is proportional its electromotive force of the circuit and inversely proportional to the resistance of the circuit. Increase of electromotive force increases current, decrease of resistance increases current flow and increase of resistance decreases current.