Combination of Resistors in Series and Parallel

The component that is used to limit the passage of charge in most electronic circuits is commonly known as a resistor. Resistors are an important part of electric circuits. The term “resistance” refers to a measurement of charge flow restriction by the resistor. Most circuits use several resistors to govern the passage of charges in a circuit. 

The process of pairing more than one resistor in a specific manner to get the desired resistance is termed the combination of the resistors. The two most basic resistor combining patterns are resistors in series and parallel. You can find out the overall resistance of a group of wire-wound resistors by using their individual values and how they are in combination with each other.

Combination of circuit and its requirement

To create a variety of valuable circuits, engineers unite different components. Resistors, capacitors and inductors are an essential part of electric circuits. You can calculate different factors such as voltage, resistance and inductance by these circuits. Distinct components of an electric circuit are linked in series or parallel to form different resistive networks. 

Resistors can be coupled in parallel and series across several loops in the same circuit to create a more complicated resistive network. As resistors never exist in isolation, it is critical to understand how to accomplish it. They are always part of a more extensive circuit with various resistors coupled in multiple ways. So, how can we figure out how much overall resistance there is in a series or parallel circuit of resistors?

Series combination of resistors

As the name suggests, a series combination has a series of different resistance. You need to arrange all the resistors in a single line. In a series combination, you can connect the resistors end-to-end. Leave the first end of the first resistor free. Connect the second end of the first resistor to the first end of the second resistor. Repeat the same with the third, fourth and other resistors you want to combine in the circuit. Then, connect the free ends of the first and last resistance to the voltage source. Now, the series combination of resistors circuit is complete. 

Properties of the resistors in a series combination circuit

• The equal current flows through each resistance. 

• The current through the individual circuit and the total current in the circuit are equal.

• The value of voltage across each resistance will be different.

• The circuit’s total resistance will equal the sum of individual resistances.

Let’s understand by example. Assume there are n resistors in the series having resistance values, respectively, R1, R2, R3,………., Rn. The voltages across the resistors are, respectively, V1, V2, V3,……….., Vn.

As we know, in series combination total voltage:

V = V1 + V2 + V3 +………….. +Vn

IR = I1R1 + I2R2 + I3R3 +……..+ InRn

Since I1 = I2 = I3 =……….. = In = I

Therefore, IR = I (R1 + R2 + /R3 +………..+ Rn)

The total current through the circuit

R = R1 + R2 + /R3 +………..+ Rn

Hence, we find that the value of total resistance in a series circuit of resistors is equal to the sum of each resistance.

Parallel combination of resistors

In a parallel combination of resistors, you need to parallel all the resistors. You must put the resistors in a single column to get a parallel combination. To do so, first of all, connect all the first ends of the resistors together. Then, combine the rest of the second ends of each resistor. Now, apply a voltage source across all resistors.

Properties of the parallel combination of resistors

• Since there is no voltage division across the circuit, the absolute voltage difference will be the same as each resistor has. Alternatively, you can say each resistor in parallel has the same voltage, which is equal to the source voltage. 

• The total current will divide across the resistors. Therefore, each resistor will carry a different amount of current.

• The inverse value of the circuit’s total resistance will equal the sum of the inverse of the resistances each individual carries. 

In a circuit of n resistors, assume that the total source voltage is V, equal for all n resistors. Again, the current through each resistor is I1, I2, I3,………, In. The total flowing current in the circuit is I. R1, R2, R3,…….., Rn are the resistance values of each resistor in the circuit. 

I = I1 + I2 + I3+……………. + In

V/R = V1/R1 + V2/R2 + V3/R3 +………..+ Vn/Rn

Since V1 = V2 = V3 =………..= Vn = V

So, V/R = V(1/R1 + 1/R2 + 1/R3 +………..+1/Rn)

Then, the total resistance  1/R = 1/R1+1/R2+1/R3+…….+1/Rn

Hence, the inverse of the total resistance in parallel combination is the sum of the inverse resistances of participating resistors.

Conclusion

You can arrange any number of resistors in series and parallel combinations by putting them into a specific arrangement. You can also create mixed circuits of series and parallel combinations of the wire-wound resistors. When solving such a hybrid circuit, you need to pay attention to where the current is dividing and where the voltage is dividing. By keeping these concepts of series and parallel combinations in your mind, you can solve any complex circuit and get to know the value of the remaining parameters. As resistors are an important part of an electric circuit, solving such combination resistors circuits is quite interesting. So, use these concepts and enjoy your learning.