# Electrical Resistance in Serial and Parallel Networks

### 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:

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