Resistors in series parallel

We defined the term “resistance” and outlined the basic design of a resistor in current and resistance. A resistor is an ohmic device with V = IR that limits the passage of charge in a circuit. In most circuits, there are many resistors. When numerous resistors are linked to a battery, the current supplied by the battery is determined by the circuit’s equivalent resistance.

The individual values of a set of resistors, as well as their connections, determine their equivalent resistance. Series and parallel connections are the most basic resistor pairings. 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 of the resistor leads on one side of the resistors are connected together in a parallel circuit, and all of the resistor leads on the other side are connected together. Each resistor in a parallel design has the same potential drop across it, and the currents through each resistor might vary depending on the resistance. The total current flowing via the parallel connections is equal to the sum of the individual currents.

Series and parallel circuit

Electrical networks and two-terminal components can be connected in series or parallel. The resulting electrical network will have two terminals and can be set up in either a series or parallel topology. Whether a two-terminal “thing” is an electrical component (e.g., a resistor) or an electrical network is a question of perspective.

Connected components have a single ‘electrical route’ and they all receive the same current from the network. The voltage throughout the network is equal to the sum of the voltages across each component. There are numerous paths in parallel connections, and each component has the same voltage across it, which is the same as the voltage throughout the network. The overall current flowing through the network is equal to the sum of the currents flowing through each component.

The two statements above are equivalent except for the role of voltage and current.

        All of the components in a series circuit are connected in series, whereas all of the components in a parallel circuit are connected in parallel. A combination of series and parallel circuits can be used to analyse many circuits and various configurations.

         A series circuit has the same current flowing through each component, and the voltage across the circuit equals the sum of the individual voltage drops across each component. In a parallel circuit, the voltage across each component is the same, and the total current is equal to the sum of the currents flowing through each component.

Circuit components

Conductors (wire), a power source, a load, a resistor, and a switch make up a circuit. The start and stop positions of a circuit are the same. As a conductor, copper wire with no insulation is often employed.

A switch is a device that is used to open or close a circuit. The flow of electric current in a circuit is controlled by resistors. A resistor is a passive component, which implies it just consumes but not generates power. A load in a circuit consumes electrical energy and converts it to light, heat, and other types of energy. A load might be anything from a light bulb to a fan. 

Need of a combination circuit

Distinct components in an electric circuit are connected in series or parallel to form different resistive networks. To make a more sophisticated resistive network, resistors can be connected in parallel and series over multiple loops in the same circuit. These circuits are known as mixed resistor circuits. However, the entire resistance should be known at the conclusion of the day. That’s vital to understand how to do it since resistors never exist in isolation. They’re always part of a larger circuit that includes a variety of resistors connected in a number of ways.

Resistor in series

When the same amount of current passes through the resistors, the circuit is said to be linked in series. In such circuits, the voltage across each resistor varies. The entire circuit is turned off if any resistor in a series connection is broken or if a fault occurs. The construction of a series circuit is simpler than that of a parallel circuit.

The overall resistance in the circuit above is expressed as:

Rtotal = R1 + R2 + ….. + Rn

The system’s overall resistance is simply the sum of individual resistances.

Take, for example, the following example problem.

A 100 ohm electrical resistance resistor is connected to a 200 ohm electrical resistance resistor. Both resistances are connected in a chain. What is the overall resistance of the system?

R1 = 100 ohm and R2 = 200 ohm in this case.

Rtotol = 100 + 200 = 300 ohm 

 Resistors in parallel

When the voltage across the resistors is the same, the circuit is said to be linked in parallel. When the branches of such circuits converge at a common location, the current is branched out and recombined. A resistor or any other component can be easily connected or disconnected in a parallel circuit without affecting the other elements.

The diagram above demonstrates a parallel connection of ‘n’ resistors. The total resistance is given by the following equation.

1Rtotal=1R1+1R2+…+1Rn

The total of the reciprocals of each individual resistor determines the overall reciprocal resistance of the system.

What if the resistors were linked in parallel instead of series in the aforementioned problem? In that scenario, what is the overall resistance?

1Rtotal=1100+1200

=200+10020000

=30020000

Therefore, 

Rtota=20000300=66.67 ohm

Conclusion

• Conductors (wire), a power source, a load, a resistor, and a switch make up a circuit.

• Resistors regulate the flow of electric current in a circuit.

• When the same amount of current passes through the resistors, the circuit is said to be linked in series.

• The total resistance of a series circuit can be calculated using the following formula:

Rtotal = R1 + R2 + … + R4 + Rn

• When the voltage across the resistors is the same, the circuit is said to be linked in parallel.

• The total resistance of a parallel circuit can be calculated using the formula below:

1Rtotal=1R1+1R2+…+1Rn

To make a more sophisticated resistive network, resistors can be connected in parallel and series over multiple loops in the same circuit. These circuits are known as mixed resistor circuits.