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).
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 R1 and R2 are connected at B point and R2 and R3 resistor are connected at C point for resistance series circuit. A is first point of R1 resistor and D is ending point of R3 resistor.
Equivalent series resistance:
Consider Voltages of A, B, C and D points are VA, VB, VC and VD. Where VA > VB
Consider, same current I flows through each resistor. Now applying Ohm’s law different parts in the circuit.
Between A and B point, VA – VB = IR1
Between B and C point, VB – VC = IR2
Between C and D point, VC – VD = IR3
Adding A to D point,
VA – VD = I (R1 + R2 + R3 )—————– (i)
If we replace R1, R2, and R3 resistance by RS as equivalent resistance.
Let, current I flows across the circuit. Then we will get same voltage between A and D point, So RS is the equivalent resistance of series resistance.
Applying Ohm’s law for resistors series,
VA – VD = IRS ———————- (ii)
From equation (i) & (ii),
IRS = I (R1 + R2 + R3)
Or, RS = R1 + R2 + R3 + ———————–+ Rn
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, R1, R2, R3 resistors one point is connected at A point and another point is connected at B.
Equivalent resistance: Consider, VA and VB are the potential difference of A and B point and VA>VB. Total current I supplies. Entering current divides into 3 branches as I1, I2, I3 and flow over R1, R2, R3. Then I meet at B point.
Consider, I1, I2 and I3 are the currents across R1, R2 and R3 resistors.
I = I1+ I2+I3 ————- (i)
Applying Ohm’s law between A and B points for three branches,
I1 = VA-VB / R1
I2 = VA-VB / R2
I3 = VA-VB / R3
Substituting values of I1, I2 and I3 in equation in (i),
I = VA-VB / R1 + VA-VB / R2 + VA-VB / R3
I = (VA-VB) (1 / R1 + 1/ R2 + 1 / R3 ) ————- (ii)
Replacing RP for R1, R2 and R3 where potential difference is same for A and B points. Total current I will be flowed across RP resistance.
Applying Ohm’s law again for equivalent resistance parallel we get,
I = VA-VB / RP ————- (iii)
From (ii) & (iii)
VA-VB / RP = (VA-VB) (1 / R1 + 1/ R2 + 1 / R3 )
Or, 1 / Rp = 1 / R1 + 1/ R2 + 1 / R3 +…………….
This is the parallel equation of resistance.
For n number of resistor which are parallel connected
1 / Rp = 1 / R1 + 1/ R2 + 1 / R3 +……………..+1 / Rn