The resistor is most important equipment in electric circuit It controls current so the study of combination is also important. There are two types of combinations.
- Resistors in series
- Resistors in parallel
1) Resistors in series:
When we connect one terminal of resistor one to another resistor, such combination is called as resistor in series. If there are numberof resistors connected in series then we need to find there equivalent resistance.To study this, construct a circuit as shown in fig.
Connect two resistors R₁ and R₂in series across the battery having voltage V. Total voltage ‘V’ drops at R₁ and R₂. Let V₁ drops at R₁ and V₂ drops at R₂.
V = V₁ + V₂. ———-1
Suppose current I flows through battery. There is only one path for flowing current, so same current will flow in both the resistors.
According to ohm law,
V₁ = I x R₁ and v₂ = I x R₂
Put this value in equation 1
I x Rₛ = I x R₁ + I x R₂
Rₛ= R₁ + R₂
Where Rₛ is equivalent resistance in series combination.
Similarly you can calculate equivalent resistance of three resistor connected in series.
Rₛ= R₁ + R₂ + R₃
If n resistors of same resistance of R connected in series then there equivalent resistance is nR.
Q1) Calculate equivalent resistance, if three resistors having resistance 4Ω, 6 Ω and 8 Ω are connected in series.
Q2) If 100 resistors of 4 Ω resistance connected in series then calculate equivalent resistance.
2) Resistors in parallel:
When we connect two terminals of each resistor together then such combination is called as parallel combination.
To study parallel combination of resistor, construct a circuit as shown in fig
Connect resistors R₁ and R₂ parallel to battery. Voltage drop across two resistors is same because they applied to same terminals of the battery. Suppose current flowing through battery is I. When current reach at point p then it split up intoI₁ and I₂.
I = I₁ + I₂————1
According to Ohms law,
V = I × Rₚ
I = V/Rₚ ———2
Where Rₚ is equivalent resistance in parallel combination.
Similarly we can calculate current flowing through R₁ and R₂ using ohms law
I₁ = V/R₁ And I₂ = V /R₂
Put this value of I,I₁ and I₂in equation 1
V/ Rₚ= V/R₁ + V /R₂
1/ Rₚ = 1/R₁ + 1 /R₂
This is the formula for calculating equivalent resistance in parallel combination.
Similarly You can calculate equivalent resistance of three resistor connected in parallel.
1/ Rₚ = 1/R₁ + 1 /R₂ + 1/R₄
Q) calculate equivalent resistance of resistors 2 Ωand 4 Ω connected in parallel.
Note: if n resistors having resistance R Ω
Are connected in parallel then there resultant will be R/n.
Difference between series and parallel combination of resistor
Series combination |
Parallel combination |
Equivalent resistance will be greater than individual |
Equivalent resistance will be smaller than individual |
Current flowing through each resistance is same |
Current flowing through each resistance is different |
Voltage across each resistor is different |
Voltage across each resistance is same |
Rₛ = R₁ + R₂ + R₃ +—–+Rₙ |
1/Rₚ = 1/R₁+ 1/R₂ +1/R₃+—-+ 1/Rₙ |
Examples- fuse, Ammeter |
Examples heater, bulb, voltmeter |
Q) Find equivalent resistance between point A and B