| Direction of conventional current is taken from higher potential to the lower potential.
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RESISTANCE
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| Opposition offered by the material of conductor in the flow of electric current is called resistance.
Resistance opposes the flow of current through a conductor. Resistance of a conductor is due to the collision of free electrons with the atoms of the conductor.
It is denoted by “R” |
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FACTORS ON WHICH RESISTANCE DEPENDS
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| (1) Length of conductor |
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| Resistance of a conductor is directly proportional to the length of conductor . |
| R a L…………….(a) |
| (2) Area of cross section of conductor |
| Resistance of a conductor is inversely proportional to area of cross section of conductor. |
| R a 1 / A……………….(b) |
| Combining (a) and (b) |
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| Where
r = resistivity of material of conductor |
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RESISTIVITY
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| Resistivity is an electrical property of material .
It is defined as the resistance of a material or conductor of 1 cubic meter volume.
Or
It is the resistance of a conductor of unit length and unit area.
Or
Resistivity of a conductor is the resistance of 1 meter long conductor whose area of cross section is
I meter square |
| Unit:
r = ohm x m
Different materials have different values of resistivity. A very high value of resistivity indicates high electrical resistance
RESISTANCE AND TEMPERATURE
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| Resistance of a conductor is directly proportional to temperature.
Reason : With the increase in temperature, vibrational motion of the atoms of conductor increases. Due to increase in vibration, probability of collision between atoms and electrons increases. As a result, resistance of conductor increases. |
| VARIATION IN RESISTANCE OF A MATERIAL AT DIFFERENT TEMPERATURES: |
| (1) Increase in resistance of a conductor is directly proportional to original resistance.
DR  R1..............(a)
(2) Change in resistance is directly proportional to change in temperature.
DR DT………….(b)
Combining (a) and (b)
DR R1 DT
DR = (constant) R1DT
Here constant = a
DR = a R1DT
Where a = temperature coefficient
As DR = R2 - R1
and
DT = T2 -T1
We get
R2 – R1 = aR1 (T2 – T1)
R2 = R1 + aR1 (T2 – T1)
R2 = R1 {1 + aT2 – T1)}When T1 = 0 and T2 = t
Rt = R0 [1 + a((t – 0)]
Rt = R0 {1 + at} |
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TEMPERATURE COEFFICIENT
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| Fractional change in resistance per unit original resistance per degree change of temperature is called temperature coefficient |
| DR = aR1DT
a = DR / R1 DT |
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UNIT
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| 1/ K OR 1/ 0C
OHM'S LAW
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INTRODUCTION
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| Ohm’s law is a quantitative relation between the potential difference across the ends of a conductor and electric current flowing through it. |
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STATEMENT
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According to Ohm’s law,
"The electric current passing through a conductor is directly proportional to the potential difference between the ends of conductor, if physical conditions of conductor remain constant."
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I a V
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MATHEMATICAL REPRESENTATION
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| According to Ohm’s law, |
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I a VI = kV
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| Where K = constant and it is called conductivity of material of conductor. |
V = I/K
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or
V = I x 1/K
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| [ but 1/K = R (resistance of conductor)] |
V = I x R
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GRAPHICAL REPRESENTATION
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Graph between electric current and potential difference is a straight line.
SERIES COMBINATION OF RESISTORS
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CHARACTERISTICS
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|  In series combination of resistors there is only one path for the flow of electric current.
Electric current passing through each resistor is same.
Potential difference across each resistor is different and it depends upon the value or resistance.
Equivalent resistance of circuit is always greater than any of the resistance connected in the circuit. |
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DISADVANTAGE OF SERIES COMBINATION
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In series combination, if one resistance is damaged then the other resistors will not work.
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EQUIVALENT RESISTANCE OF CIRCUIT
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| Consider three resistances R1, R4 and R3 connected to one another in series circuit as shown below. |
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| Let the circuit is connected to a power supply of voltage 'V' and an electric current 'I' is passing through the circuit. |
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Potential difference across R1 is V1
Potential difference across R2 is V2
Potential difference across R3 is V3
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| The sum of these Potential differences is equal to 'V'. |
V = V1 + V2 + V3
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According to Ohm's law V = IR
Putting the value of V, we get, |
IRe = IR1 + IR2 + IR3
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| OR |
Re = R1 + R2 + R3
PARALLEL COMBINATION OF RESISTORS
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CHARACTERISTICS
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| In parallel combination of resistors there are more than only one paths for the flow of electric current.
Electric current passing through each resistor is different and it depends upon the value or resistance.
Potential difference across each resistor is the same.
Equivalent resistance of circuit is always smaller than any of the resistance connected in the circuit. |
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ADVANTAGE OF PARALLEL COMBINATION
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In parallel combination, if one resistance is damaged then the other resistors will work properly because there are more than one path for the flow of electric current.
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EQUIVALENT RESISTANCE OF CIRCUIT
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| Consider three resistance R1, R4 and R3 connected to one another in parallel circuit as shown below. |
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| Let the circuit is connected to a power supply of voltage 'V' and an electric current 'I' is passing through the circuit. |
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Electric current passing through R1 is I1
Electric current passing through R2 is I2
Electric current passing through R3 is I3
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| The sum of all three currents is equal to 'I'. |
I = I1 + I2 + I3
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According to Ohm's law I = V/R
Putting the value of I, we get, |
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DEFINITION
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| We know that when electric current is passed through a conductor, energy is dissipated in the form of heat energy. Hence for maintaining a steady current continuous source of energy is required. This source when connected across the resistance maintains a P.D of constant value across its ends |
| and hence supplies energy at the rate at which it is dissipated. The devices such as dry cell, battery or electric generator are the source of emf .This strength of these sources is known as emf. |
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| Suppose “q” coulomb of charge requires an amount of work “W” joule to be transported through the source then emf in volts is given by: |
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EMF = W / q
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| EMF AND TERMINAL POTENTIAL DIFFERENCE |
| Consider a source of emf connected to a resistance “R” through which a steady current “I” flows as shown below: |
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| Let the emf of source is E
Potential difference across resistance R is V |
| We know that |
| A source of emf also has some resistance which is due to electrolytes and electrodes. Therefore some useful energy of emf-source is used in passing the current through the source. |
| Let the internal resistance of the source is “r” |
| Potential drop across emf source = Vr |
| Since |
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| Where V = terminal potential difference
When no current is drawn from the source then emf and terminal potential difference are equal.
If the current is passing through the circuit then the terminal potential difference is less than that of the emf of the source.
Power Dissipation in Resistors
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| When an electric current passes through a conductor, some useful electrical energy is dissipated in the form of heat energy. This loss of electrical energy is due to the collision of charges with the atoms of conductor. Loss of electrical energy in unit time is referred to as "power dissipation in resistor". |
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EXPRESSION FOR POWER LOSS
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| Let 'q' amount of electric charge passes through a conductor in unit time, the electric current through the conductor is given by: |
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I = q/t
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| Or |
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q = I x t ............... (1)
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| During the flow of electric current energy lost in the form of heat is equal to q x V, where V is the potential difference across the ends of conductor. |
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Energy lost = q x V
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| Putting the value of q, we get |
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Energy lost = I x t x V
Energy lost/t = VI
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| But Energy /t = Power |
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Power = VI
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POWER LOSS IN TERMS OF CURRENT AND RESISTANCE
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| According to Ohm's law V = IR. putting the value of V, we get |
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Power = (IR)I
Power = I2R
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POWER LOSS IN TERMS OF RESISTANCE AND POTENTIAL DIFFERENCE
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| As power = VI and according to Ohm's law I = V/R, putting the value of i, we get |
Power = VI
Power = V (V/R)
Power = V2/R
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UNIT OF POWER
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In SI system unit of power is Watt.
Other large units are:
1. Kilowatt KW (1000 watt)
2. Megawatt W(106 watt) |
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