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Resistors in Series and Parallel Configuration

Electric current is caused due to the movement of charged particles. When the charged particles move in a specific direction at a particular speed, this results in the formation of an electric current. And the flow of electric current results in the generation of electricity. Furthermore, electric current flow is constant and stable. Therefore, we can observe the electric current flowing from a higher potential to a lower potential in an electric circuit.

Resistor

A regular electric circuit consists of a conductor, resistor, switch, and power source. The resistor is one of the crucial parts of an electric circuit. It limits the flow of current in an electrical circuit, thus, preventing the circuit from damage. Whenever there is a high current flow in the circuit, the resistor limits the excessive current flow.

We use a particular combination to place these resistors in a circuit. The combination depends upon the function, need and requirement of the resistors in the circuit. For example, if we need to control the current in the circuit, we may use a different combination than what we need to control the current to save our appliances. In some cases, we may use a combination of resistor placing for current control and saving our appliances.

Combination of resistors

The electricians use a combination of resistors. The combination may be series or parallel. We refer to resistors' series or parallel connection with respect to their connection with the main power supply. Let us study the series and parallel connection in detail.

Series combination

In a series connection, the current passes through each of the resistors, one at a time. This means each resistor will have the same amount of current flow through them. Therefore, in a series connection, there will be a voltage drop across every resistor. Therefore, a series combination is used when we need to control the voltage within an electrical circuit.

We can calculate the equivalent resistance of the entire series combination. To derive the equivalent resistance relation, we will use Ohm's law. According to Ohm's law, the potential drop in an electrical circuit, V, is given by,

V = IR
Where I = current
R = resistance
According to the Kirchhoff’s law, we have,
i=1NVi = 0
V – V1 – V2 – V3 = 0

Since the current flowing across the circuit in a series combination is same, therefore,
V = IR1 + IR2 + IR3
V = I (R1 + R2 + R3)
This implies that the total resistance is equal to the sum of individual resistance in a series combination. Therefore, for N number of resistors,
Req (series) = R1 + R2 + R3 + … + Rn
Since the entire current must pass through every resistor to resist the current flow within an electrical circuit, every resistor is added.

Parallel combination

When we need to control the current, we use a parallel combination. In this, the current flowing through each branch in an electrical circuit is reduced, but the voltage drop remains the same in every leg of the electrical circuit. There are more resistors connected in parallel than series in a household. This is because if one appliance is damaged, the other must function. This is possible only in a parallel connection.
We will use Ohm’s law to find the equivalent resistance. According to Ohm’s law,
V = IR
According to Kirchhoff’s law,
Iinput = Ioutput
I = I1+ I2 + I3
I = V1R1 + V2R2 + V3R3

Since the voltage drop in a parallel combination remains the same, therefore,
I = VR1 + VR2 + VR3
= V (1R1 + 1R2 +1R3)
Req (parallel) = (1R1 + 1R2 +1R3 + …1Rn) -1

Combination of series and parallel connection

We also use the combination of series and parallel connections when there are too many electrical connections in a household. To save appliances from damage, these combinations are necessary to be used in an electrical circuit. The main goal to use these combinations is to reduce the number of resistors in a circuit. We can calculate the equivalent resistance using series and parallel formulas and apply them separately on each circuit branch.

Example: Three resistors R1 = 1 Ω, R2 = 2 Ω, and R3 = 2 Ω, are connected in parallel. The battery has a voltage of 3V. Calculate the equivalent resistance, and current through the circuit.
Solution:

The equivalent resistance in a parallel combination is given as,
Req (parallel) = (1R1 + 1R2 +1R3 + …1Rn) -1
= (11 + 12 +13) -1
Req = 0.5 Ω
From Ohm’s law, I = V / Req
= 3 / 0.5 = 6A

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