# Electrical Resistance in Serial and Parallel Networks

## Resistors in parallel and serial connections

### Serial Connection

The total resistance for resistors connected in series can be calculated as

*R = R _{1} + R_{2} + .... + R_{n} (1)*

*where *

*R = resistance (ohm, Ω)*

#### Example - Resistors in Series

Three resistors *33 ohm*, *33 ohm* and *47 ohm* are connected in serial. The total resistance can be calculated as

*R = ( 33 ohm) + (33 ohm) + (47 ohm) *

* = *113 ohm

### Parallel Connection

The total resistance for resistors connected in parallel can be calculated as

*1 / R = 1 / R _{1} + 1 / R_{2} + .... + 1 / R_{n} (2)*

Equivalent resistance of 2 resistors connected in parallel can be expressed as

*R = R_{1} R_{2} / (R_{1} + R_{2})_{} (3)*

#### Example - Resistors in Parallel

Three resistors *33 ohm*, *33 ohm* and *47 ohm* are connected in parallel. The total resistance can be calculated as

*1 / R = 1 / ( 33 ohm) + 1 / (33 ohm)_{ } + 1 / (47 ohm)*

* = 0.082 (1 / ohm)*

*R = 1 / (0.082 ohm) *

* = 12.2 ohm*

If the battery voltage is *12 V* - the current through the circuit can be calculated by using Ohm's law

*I = U / R*

* = (12 V) / (12.2 ohm)*

* = 0.98 ampere*

The current through each resistor can be calculated

*I _{1} = U / R_{1 }= (12 V) / (33 ohm) = 0.36 ampere*

*I _{2} = U / R_{2 }= (12 V) / (33 ohm) = 0.36 ampere*

*I _{3} = U / R_{3 }= (12 V) / (47 ohm) = 0.26 ampere*

### Resistors Connected in Parallel - Calculator

Add the resistances for up to five parallel connected resistors and (optionally) the circuit voltage.

The total resistance and current - and the individual currents in all resistors - will be calculated:

*R _{1} (ohms)*

*R _{2} (ohms)*

*R _{3} (ohms)*

*R _{4} (ohms*)

*R _{5} (ohms)*

*Voltage (V)*

*I _{1} (amps)*

*I _{2} (amps)*

*I _{3} (amps)*

*I _{4} (amps)*

*I _{5} (amps)*

**R (ohms) **

* **I (amps)*

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