# 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 *

Standard resistors are available with

- resistances from 0.0002 Ω through 1012 Ω
- power ratings from 1/8 watt through 250 watts
- accuracies from 0.005% through 20%

### 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:

### Power Dissipated by a Resistor

The power dissipated by a resistor can be expressed as

*P = U I *

* = R I ^{2} *

* = U ^{2} / R (4)*

*where*

*P = power (W, Js)*

### Thévenin Equivalent Circuit

Thévenin’s theorem states that

- any two-terminal network of resistors and voltage sources is equivalent to a single resistor R in series with a single voltage source V.

The voltage divider can be regarded as a Thévenin Equivalent Circuit where the internal arrangement of resistors and the input voltage source equivalents so a single source and a single resistor.

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