Resistance:
The property of a substance which offers opposition to the flow of current through it is called its
resistance.
This opposition comes from the collisions of moving electrons with atoms of the substance.
Unit of Resistance: ohm (Ω)
The SI unit of resistance R is ohm.
If we put V = 1 V, and I = 1 A, the value of R will be 1 Ω.
Thus When a potential difference of one volt is applied across the ends of a conductor and one ampere of current passes through it, then its resistance will be one ohm.
Ohm’s law
If V is the potential difference across the two ends of any conductor, then current I will flow through it. The value of the current changes with the changes in potential difference and
is explained by Ohm's law, stated as:
The amount of current passing through a conductor is directly proportional to the potential difference applied across its ends, provided the temperature and the physical state of the
conductor does not change.
$$ V \propto R $$
$$ or \;\;\;\; V = IR $$
where R is the constant of proportionality and is the resistance of the conductors. Its SI unit is ohm and is denoted by a symbol Ω.
If a graph is plotted between the current I and the potential difference V, a straight line will be obtained.
Series Combination
Two or more resistors are said to be connected in series when the same amount of current flows through all the resistors. In such circuits, the voltage across each resistor is different.
Equivalent Resistance of Series Circuit
The total voltage in a series circuit divides among the individual resistors so the sum of the voltage across the resistance of each individual resistor is equal to the total voltage supplied by the source.
Thus, we can write as
$$ V= V_{1}+ V_{2} + V_{3} \;\;\;\; \cdot \cdot \cdot \cdot (1) $$
where V is the voltage across the battery, and V1, V2, V3 are the voltages across resistors R1, R2 and R3 respectively. If I is the current passing through each resistor, then from Ohm's law
$$V= IR_{1}+IR_{2}+IR_{3}$$
$$V= I(R_{1}+R_{2}+R_{3} ) $$
We can replace the combination of resistors with a single resistor called the equivalent resistance Re such that the same current passes through the circuit. From Ohm's law
$$ V= I R_{e}$$
Thus, Eq. 1 becomes
$$I R_{e} = I(R_{1}+R_{2}+R_{3} ) $$
$$ R_{e}= R_{1}+R_{2}+R_{3} \;\;\;\; \cdot \cdot \cdot \cdot (2) $$
Thus, the equivalent resistance of a series combination is equal to the sum of the individual resistances of the combination.
If resistances R1+R2+R3, ………….. , Rn are connected in series, then
the equivalent resistance of the combination will be given by
Re = R1+R2+R3, ………….. , Rn
Parallel circuits have two big advantages over series circuits.
1. Each device in the circuit receives the full battery voltage.
2. Each device in the circuit may be turned off independently without stopping the current flowing to the other devices in the circuit. This principle is used in household wiring.