## Parallel & Series

Resistance

Parallel Resistance | XXXX Ω |

Series Resistance | XXXX Ω |

Resistance 1: |
Ω | |

Resistance 2: |
Ω | |

Resistance 3: |
Ω | |

Resistance 4: |
Ω | |

Resistance 5: |
Ω | |

Resistance 6: |
Ω | |

Resistance 7: |
Ω | |

Resistance 8: |
Ω | |

Resistance 9: |
Ω | |

Resistance 10: |
Ω |

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# Series and Parallel Resistance Calculator

Resistance is an electrical element that does not allow the flow of current through it easily. Resistance is used in many electrical circuits and devices in our day to day life. Inside these electrical devices, the resistances are arranged in various configurations.

You must also have observed while making connections on a breadboard in your electronics lab how resistors are connected in different ways. Depending on the way their ends are connected, there are two basic types of resistance circuits:

- Series Circuits
- Parallel Circuits

As we move ahead in this post, we shall understand the working, comparison, calculations involved and differences between these series circuits and parallel circuits.

### Series Circuits

Two or more resistors are said to be connected in series if the current flowing through them is the same. In other words, the current originating from the source or the total current will not branch up in any other path but will move only in one straight path.

When resistances are connected in series, the net resistance of the circuit is the sum of all the resistances of the circuit.

The following circuit diagram shows three resistances R_{1}, R_{2} and R_{3} connected in series. The net resistance of this series circuit is R_{net} = R_{1} + R_{2} + R_{3}.

In general, if ‘n’ resistances are connected in series, the net resistance is R_{net} = R_{1} + R_{2} + …. R_{n}.

For example, if a circuit has three resistors each of 10 ohms in series, and has a 30V voltage source, then the current flowing in the circuit and through each of them is given by I = V / R = 10 / 30 = 0.33 A.

### Parallel circuits

Two or more resistors are said to be connected in parallel if they are joined with their heads on one side and tails on the other side of the circuit. In a parallel circuit, the current originating from the source or the total current will branch up at the junction where the heads of resistances meet and then flows in different quantity in each resistor and then again combines together at the meeting point of the tails of the resistors and flows towards the origin.

When resistances are connected in parallel, the inverse of the net resistance of the circuit is the sum of inverses of all the resistances of the circuit.

The following circuit diagram shows three resistances R_{1}, R_{2} and R_{3} connected in parallel. The net resistance of this parallel circuit is 1/R_{net} = 1 / R = 1 / R_{1} + 1 / R_{2} + 1 / R_{3}.

In general, if ‘n’ resistances are connected in parallel, the net resistance is:

1/ R_{net} = 1 / R = 1 / R + 1 / R_{2} + 1 / R_{3} +….+ 1/R_{n}

For example, if three resistors 4ohms, 8 ohms and 8 ohms are connected in parallel in a circuit with 10 V supply, then, the net resistance of the circuit is given by: 1/Rnet = 1/4+1/8 + 1/8 = ½ or Rnet = 2 ohms

Then the current flowing through the circuit is given by V/I = 10/2 = 5 amps.

In case you want to calculate current in each resistor, you can use Ohm's law:

Current through 4 ohms resistor I_{1}= 10/4 = 2.5 A

Current through 8 ohms resistor I_{1}= 10/8 = 1.25 A

Current through 4 ohms resistor I_{1}= 10/8 = 1.25 A

Observe that if you add the individual currents through each resistor, you will get the total current that is flowing in the circuit.

### Combination of Series and Parallel Resistors

If you find a circuit that has resistors in series and parallel, then you have to solve the resistors combination step by step considering whether they are in series or parallel with the neighboring ones and then arrive at the final resistance of the circuit.

Points about series and parallel connection of resistors:

- The effective resistance of a series circuit is always greater than each of the resistor in the circuit.
- The effective resistance of a parallel circuit is always lesser than each of the resistor in the circuit.
- The current in each of the series connected resistor is the same, while the voltage across each parallel resistor is the same.
- In a series resistors circuit, if one resistance gets damaged, the entire circuit will break and behave as an open circuit.
- In a parallel resistors circuit, if one resistor is damaged, the current keeps flowing in the other resistors and the circuit will keep working, however with a different value of net resistance.

### How does CalculatorHut’s series and parallel resistance calculator helps you?

We come across the arrangement of series and parallel combination of resistors in many places in our day to day life. For example, for lighting circuits, we use the parallel connection, while for appliances that work directly on mains, a series connection is given.

CalculatorHut, a one-stop destination of online scientific and non-scientific calculators, offers free online series and parallel resistance calculator that will solve all your online calculator needs for free. You can calculate up to ten resistors that are connected either in series or parallel using this user-friendly online free series and parallel resistance calculator. This is a very friendly tool for students and helps them to verify if their resistance calculations are correct.

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