Concept of Combination of Resistors

When two or more resistances are connected in parallel between two points and each has a different current direction, they are said to be connected in parallel. In such circuits, the current is branched out and recombined as the branches intersect at a common point.

The resistance may be arranged in two ways:

1. in series
2. in parallel

Because the output current of the first resistor flows into the input of the second resistor in a series circuit, the current in each resistor is the same. All resistor leads on one side of the resistors are connected in a parallel circuit, and all resistor leads on the other side are connected.

Combination of Resistances

A series circuit is one in which the entire current flows through all components. A parallel circuit has branches that divide the current so that only a portion of it flows through each branch. In a parallel circuit, the voltage, or potential difference, across each branch is the same, but the currents may differ. Each light or appliance in a home electrical circuit, for example, receives the same voltage, but each draws a different amount of current based on its power requirements. A series of similar batteries connected in parallel provides more current than a single battery while maintaining the same voltage. 

Introduction to Resistor

A two-terminal passive electrical component is used to limit or regulate the flow of electric current in electrical circuits. The primary function is to reduce current flow and lower voltage in a specific area of the circuit. A resistor is a component that prevents electricity from flowing. Current is the term for the flow of electricity. The value of each resistor indicates how strongly it resists current flow. The ohm is the unit of resistance, and the symbol for the ohm is the Greek letter omega: Ω

Resistors in Series Combination 

When the same amount of current flows through the resistors, the circuit is said to be connected in series. The voltage across each resistor in such circuits varies. If any resistor in a series connection is broken or a fault occurs, the entire circuit is turned off. Compared to a parallel circuit, constructing a series circuit is easier. Mathematically, the equal resistance of any range of resistances (R1, R2, R3, R4, R5, ……..) linked in the collection is given as Req = R1 + R2 + R3 + R4 + R5 + …….. Consider a case of four resistances (R1, R2, R3 and R4) linked in collection with different corresponding voltage sources (V1, V2, V3 and V4 ) in a circuit proven below:

According to diagram,  Veq = V1 + V2 + V3 

The current I through every resistor is identical, i.e.

 I = I1 = I2 = I3 

We know that,

 Veq = IReq 

By making use of Ohm’s regulation to all resistors for my part as: 

V1 = IR1

 V2 = IR2

 V3 = IR3

 Hence, 

IR= IR1 + IR2 + IR3 

Or

Req = R1 + R2 + R3  

Resistors in Parallel Combination

When two or more resistances are connected in parallel between two points and each has a different current direction, they are said to be connected in parallel. The current is branched out and recombined in such circuits as the branches intersect at a common point.

Mathematically, the equal resistance of any range of resistances (R1, R2, R3, R4, R5, ……..) linked in parallel is given as: 1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5 + ……..1/Rn

In a  case of three resistances (R1, R2, and R3) linked in parallel with different corresponding voltage sources (V1, V2, and V3) in a circuit proven below:

According to ohm’s law

 Ieq = V / Req 

On making use of Ohm’s regulation to character resistors as:

 I1 = V / R1 

I2 = V / R2 

I3 = V / R3

 Hence, 

V / Req = V / R1 + V / R2 + V / R3 

or 

1 / Req = 1 / R1 + 1 / R2 + 1 / R3 

The reciprocal of the equal resistance of a collection of resistances joined in parallel is identical to the sum of the reciprocals of the character resistances.

Conclusion 

The current flowing through each resistor in a series circuit is constant, but the voltage drop across each resistor varies. The electric potential difference across each resistor (V) is the same in parallel circuits, but current flowing is different . In a resistor, the current follows Ohm’s law: I = V / R. Because the voltage across each resistor is the same, the current will be lowest where the resistance is greatest.