An introduction to Ohm's law, Resistance and Joule’s Law

 

An introduction to Ohm's law, Resistance and Joule’s Law

     

1) Electric current :-

Electric current  is the flow of electrons through a conductor.

The device which causes the flow of electrons through a conductor is

called a cell.

Electrons flow from the negative terminal to the positive terminal.

Electric current flows from the positive terminal to the negative terminal.

This is called conventional current.  Electric circuit  is a continuous and closed path of an electric current.

Definition :- "The rate of flow of charges through a conductor or the quantity of charges flowing through a conductor in unit time."

I =  current = Q / t

where Q – quantity of charge,  t – time

The SI unit of electric charge is coulomb (C). It is the charge contained in 6x10 ¹⁸ electrons.

The SI unit of current is called ampere (A).

One ampere is the current flowing through a conductor if I coulomb of

charge flows through it in 1 second.

1ampere = 1coulomb / 1 second

Electric Current is measured by an ammeter. It is always connected in series in a circuit.

2) Electric potential and Potential difference :-

Electric current will flow through a conductor only if there is a difference in

the electric potential between the two ends of the conductor. This difference in

electric potential between the two ends of a conductor is called potential difference.

The potential difference in a circuit is provided by a cell or battery. The

chemical reaction in the cell produces a potential difference between the two

terminals and sets the electrons in motion and produces electric current.

"Potential difference  between two points A and B of a conductor is the

amount of work done to move a unit charge from A to B."

Potential difference = or V = Work done W / Charge Q

The SI unit of potential difference is volt (V).

One volt is the potential difference when 1 joule of work is done to move a

charge of 1 coulomb from one point to the other.

1 volt = or 1 V =1J / 1C

Potential difference is measured by a voltmeter. It is always connected in parallel across the two point between which the potential difference is to be measured.

3) Ohm’s law :-

Ohms law is a relationship between the potential difference across a conductor and the current flowing through it.

Ohms law defines the relationship between  voltage, current and resistance.

These basic electrical units apply to direct current, or alternating current.

Ohm’s Law is the foundation of electronics and electricity.

This formula is used extensively by electricians.

Without a thorough understanding of “Ohm’s Law” an electrician can’t design or troubleshoot even the simplest of electronic or electrical circuits.

Ohm’s law states that :-

"The current I flowing through a conductor is directly proportional to the potential difference V between its ends provided its temperature remains constant."

I α V or V α I

V = I R

Where R is a constant called resistance for a given metallic wire at a given temperature.

 

Quantity	Symbol	Unit	Unit Symbol
Current	I	ampere	A
Voltage	V	volt	V
Resistance	R	ohm	Ω

   From triangle, we have formula

 1. For Voltage           V = I R    

2. For Current              I = V / R         

3. For Resistance        R = V / I 

4a) Resistance :-

Resistance is the property of a conductor to resist the flow of current through it.

According to Ohm’s law              R = V / I

The SI unit of resistance is ohm (Ω).

If the potential difference across the two ends of a wire is 1 V and the current flowing through it is 1 A then the resistance R of the conductor is 1 ohm (1 Ω ).

1  ohm  = 1 volt / 1 ampere

The current flowing through a resistor is inversely proportional to the resistance. So if the resistance is doubled, then the current gets halved.

4 b) Factors on which the resistance of a conductordepends :-

The resistance of a conductor depends upon its:-

i) Length

ii) Area of cross section

iii) Material of the conductor.

   Resistance is directly proportional to the length l of the conductor and inversely proportional to the area of cross section A of the conductor.

R α l  and  R α 1 /A

R α l / A or R = ρ l / A

ρ = R. A / l

Where ρ (rho) is a constant of proportionality and is called Resistivity of the material of the conductor.

The SI unit of resistivity is ohm meter ( Ωm).

Conductors like metals and alloys have low resistivity 10^-8 Ωm to 10^-6 Ωm.

Insulators like rubber, glass etc. have high resistivity 10¹² Ωm to 10¹⁷ Ωm.

 

5a) Resistors in series :-

When three resistors R₁, R₂ and R₃ are connected in series across AB

1.  The current I in all the resistors is the same.

2.  The total voltage (V) across the resistors is equal to the sum of the voltage across each resistor.

V = V₁ + V₂ + V₃

I . R_S  = I . R₁ + I . R₂ + I . R₃

3.  The equivalent resistance is the sum of the resistances of each resistor.

R_S = R₁ + R₂ + R₃

 

5 b) Resistors in parallel :-

When three resistors R₁, R₂ and R₃ are connected in parallel across AB,

1.  The voltage (V) in all the resistors is the same.

2.  The total current in all the resistors is the sum of the current in each

resistor.

I = I₁ + I₂ + I₃

V / R_p = 1/ R₁ + 1/ R₂ + 1/ R₃

3.  The reciprocal of the equivalent resistance is the sum of the

reciprocals of each resistance.

1/ R_p =  1 / R₁ + 1 /R₂  + 1 /R₃

5c )Difference between series and parallel combination of resistances:

Series circuit

1.     The current in each resistor have the same value.

2.     The total voltage drop is equal to the supply voltage.

3.     The effective resistance is always more than the minimum value resistance in the series circuit.

Parallel circuit

1.     The voltage across each resistor is equal to the supply voltage.

2.     The total current in the circuit is equal to the sum of the current in individual parallel circuit.

3.     The effective resistance is always less than the minimum value resistance in the parallel circuit.

 

6) Heating effect of electric current :

When electric current is supplied to a purely resistive conductor, the energy of electric current is dissipated entirely in the form of heat and as a result, resistor gets heated. The heating of resistor because of dissipation of electrical energy is commonly known as Heating Effect of Electric Current.

Joule's law:

 "When an electric current passes through a conductor, heat H is produced, which is directly proportional to the resistance R of the conductor, the time t for which the current flows, and to the square of the magnitude of current I."

H α R  ;     H α t  ;     H α I²   

H α  I²  .R . t

H = I²  .R . t /J 

This is formula for Joule's law ,where J is Joule's constant = 4.2 J / cal.

 

7) Electrical energy and Electric power :-

     1 .Electrical energy is the work done to maintain the flow of current in a       conductor.

H = W = I² . R .t

The unit of electrical energy is joule (J).

​

      2.  Electric power :- is the rate at which electric current is used.

Power = Work done / time ;   P = W /t    but W = I² . R .t

 

Power P = I²R

but  R = V / I ;                            P =  V. I

 

The SI unit of power is watt (W).

   "One watt is the power when 1A of current flows across a potential

difference of 1V."

1kWh = 1000 watt x 3600 seconds = 3.6 x 10⁶ joules

The commercial unit of power is watt hour (Wh) or kilo watt hour (kWh).

One kWh is the power consumed when 1W of power is used for 1 hour.