Resistor |
Definition of resistance
The property of a material to resist the free flow of electrons through it is called resistance. It is denoted by R. Resistance of a material depends on its cross-sectional, length and relative permeability.
Resistance of a material is given by R = ρ ^{l}/_{A}
where,_{ }ρ is the relative permeability of the material, l is the length of the material and A is its cross sectional area.
_{}
Symbol of resistance:
Symbol of Resistance |
Ohm’s law:
According to ohm’s law, current flowing through a resistance is directly proportional to the voltage across it.
V = IR >> R= ^{V }/ _{I}
V- Voltage across the resistor
I - Current flowing through it.
When current flows through a conductor few electrons lose their energy due to collision with the atoms in it. The energy lost due to collision is dissipated in the form of heat.
Unit of resistance:
The unit of resistance is ohm and the unit of resistance is symbolically represented as Ω.
Power absorbed by the resistor
The power absorbed by the resistance is
P=VI = I (IR) = I^{2}R
Where,
V is the voltage across the resistor and I is the current flowing through it.
Energy lost across a resistor
Energy lost across a resistor in a time t is given by
E= (V^{2 }/ R) t = I^{2}Rt
“V” is the voltage across the resistor, “I” is the current flowing through it and “t” is time in seconds.
Problems based on resistance.
Problem 1:
A 20 ohm resistance is connected across a 12V battery. Calculated the power lost and the energy lost in the circuit when it is kept closed for 3 minutes.
Solution:
Current flowing though the resistor R= ^{V }/ _{I}
= 12/20 = 0.6A
Power lost across the resistor, P = I^{2}R
= 0.6^{2} x 20 = 7.2 Watts
Energy lost in the resistor, W= I^{2}R x t
= 7.2 x 3x 60s
= 1296 Joules
Problem 2
If a resistance connected across a 6V battery allows a current of 0.2 ampere through it, find the value of resistance.
Solution
According to ohm’s law,
R= ^{V }/ _{I}
_{ = 6/0.2}
_{ } = 30 ohms.
Resistance connected in series.
Resistance connected in series. |
In a series circuit current through all the elements is equal. Let V_{1}, V_{2}, V_{3}, … V_{n} be the voltage across each resistance. Then total voltage across the series connected resistances is given by
V_{s} = V_{1} + V_{2} + V_{3} + … V_{n}
IR_{eq} = IR_{1} + IR_{2}+ IR_{3 }+ …..+ IR_{n}
Dividing the whole equaltion with I,
R_{eq} = R_{1} + R_{2}+ R_{3 }+ …..+ R_{n}
From the above equation it is evident that in a series connection of resistances, the total resistance is equal to the sum of the individual resistances.
Resistance connected in parallel.
In a parallel circuit voltage across every branch is equal. Let I_{1}, I_{2}, I_{3}, … I_{n} be the current across each resistance. Then total current across the series connected resistances is given by
I_{T} = I_{1} + I_{2} + I_{3} + … I_{n}
V/R_{eq} = V/R_{1} + V/R_{2}+ V/R_{3 }+ …..+ V/R_{n}
Dividing the whole equaltion with V,
1/R_{eq} = 1/R_{1} + 1/R_{2}+ 1/R_{3 }+ …..+ 1/R_{n}
From the above equation it is evident that when a set of resistances are connected in parallel then the reciprocal of equivalent resistance is equal to the sum of reciprocal of individual resistances.
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