**Resistance definition: **Electricity means flowing of electron. If a conductor’s two points has potential difference, then negative charge flows over low voltage to high voltage. Though we know normally current flows from high potential to low potential. At the time of flowing electron makes diffraction in the conductor. As a result flowing current hinders. These types of character of conductor are resistance. It stands that the cause of flowing electric current hinders across a conductor is resistance. This is the definition of resistance. Resistance measurement is easy. Division of total voltage and current is the resistance of a resistor.

From Ohm’s law at specific temperate,

I = V / R

Or, R = V / I

At a specific temperature the division of potential difference and flowing current signifies the resistance. We can measure resistance by it.

S.I resistance unit is Ohm. International unit of flowing current is Ampere (A) and potential difference is volt (V).

So,

1 Ohm = 1V / 1A

Dependence of resistance:

Resistance of conductor depends upon many terms given below

(i) Length of conductor

(ii) Material of conductor

(iii) Temperature of conductor

(iv) Resistance temperature

(v) Area of cross section of conductor

(vi) Effect of Pressure

(vii) Effect of Light

(viii) Effect of Magnet

(ix) Purification of conductor

(x) Resistance heat

## Resistances in series

When some resistors are connected such as first resistor’s ending point connects to second resistor’s first point and second resistor’s last point connects to third resistors first point thus some resistors are connected and same current I flows through each resistor. Then we can say the combination is series combination of series resistance.

We consider given figure shown where resistance in a series circuit.

Here R_{1 }and R_{2} are connected at B point and R_{2 }and R_{3} resistor are connected at C point for resistance series circuit. A is first point of R_{1} resistor and D is ending point of R_{3} resistor.

## Equivalent series resistance:

Consider Voltages of A, B, C and D points are V_{A, }V_{B, }V_{C }and V_{D}. Where V_{A} > V_{B}

Consider, same current I flows through each resistor. Now applying Ohm’s law different parts in the circuit.

We get,

Between A and B point, V_{A} – V_{B} = IR_{1}

Between B and C point, V_{B} – V_{C} = IR_{2}

Between C and D point, V_{C} – V_{D} = IR_{3}

Adding A to D point,

V_{A} – V_{D} = I (R_{1 }+ R_{2} + R_{3 })—————– (i)

If we replace R_{1,} R_{2}, and R_{3 }resistance by R_{S }as equivalent resistance.

Let, current I flows across the circuit. Then we will get same voltage between A and D point, So R_{S} is the equivalent resistance of series resistance.

Applying Ohm’s law for resistors series,

V_{A} – V_{D} = IR_{S} ———————- (ii)

From equation (i) & (ii),

IR_{S} = I (R_{1 }+ R_{2} + R_{3})

Or, R_{S }= R_{1 }+ R_{2} + R_{3} + ———————–+ R_{n}

This is the equation of resistance in series circuit.

It means sum of all resistance is the equivalent resistance for series combination of resistance.

## Resistance in Parallel

Connecting some electrical resistor between two common points having same potential difference for each resistor between two points is known parallel combination of resistors.

Parallel resistance is shown in figure. Here, R_{1, }R_{2}, R_{3 }resistors one point is connected at A point and another point is connected at B.

**Equivalent resistance: **Consider, V_{A} and V_{B} are the potential difference of A and B point and V_{A}>V_{B}. Total current I supplies. Entering current divides into 3 branches as I_{1}, I_{2}, I_{3 }and flow over R_{1, }R_{2}, R_{3. }Then I meet at B point.

Consider, I_{1}, I_{2 }and I_{3 }are the currents across R_{1, }R_{2} and R_{3 }resistors.

I = I_{1}+ I_{2}+I_{3 }————- (i)

Applying Ohm’s law between A and B points for three branches,

I_{1 }= V_{A}-V_{B }/ R_{1}

I_{2} = V_{A}-V_{B }/ R_{2}

I_{3} = V_{A}-V_{B }/ R_{3}

Substituting values of I_{1}, I_{2 }and I_{3 }in equation in (i),

I = V_{A}-V_{B }/ R_{1 }+ V_{A}-V_{B }/ R_{2} + V_{A}-V_{B }/ R_{3}

I = (V_{A}-V_{B}) (1 / R_{1 }+ 1/ R_{2 }+ 1 / R_{3} ) ————- (ii)

Replacing R_{P }for R_{1, }R_{2} and R_{3 }where potential difference is same for A and B points. Total current I will be flowed across R_{P} resistance.

Applying Ohm’s law again for equivalent resistance parallel we get,

I = V_{A}-V_{B }/ R_{P }————- (iii)

From (ii) & (iii)

V_{A}-V_{B }/ R_{P }= (V_{A}-V_{B}) (1 / R_{1 }+ 1/ R_{2 }+ 1 / R_{3} )

Or, 1 / Rp = 1 / R_{1 }+ 1/ R_{2 }+ 1 / R_{3 }+…………….

This is the parallel equation of resistance.

For n number of resistor which are parallel connected

1 / Rp = 1 / R_{1 }+ 1/ R_{2 }+ 1 / R_{3 }+……………..+1 / R_{n}