Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

• the most efficient way to navigate the Engineering ToolBox!

# Electrical Resistance in Serial and Parallel Networks

### Serial Connection

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

R = R1 + R2+ .... + 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 / R1 + 1 / R2+ .... + 1 / R n               (2)

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

R = R1 R2/ (R1 + R2)          (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

I1 = U / R1 = (12 V) / (33 ohm) = 0.36 ampere

I2= U / R2= (12 V) / (33 ohm) = 0.36 ampere

I3 = U / R3 = (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 I2

= U2 / 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.

## Related Topics

### • Electrical

Electrical engineering with units, amps and electrical wiring. Wire gauges, electrical formulas, motors and more.

## Related Documents

### Aluminum Conductor Characteristics

Characteristics of all-aluminum conductors (AAC).

### Capacitors - Parallel and Serial Circuits

Parallel and serial connected capacitor circuits.

### Current Divider - Online Calculator

An electric current divider outputs a current that is a fraction of the input current.

### Electric Circuit Diagram - Drawing Template

Online shareable electric circuit diagram.

### Electrical Inductance - Serial and Parallel Connections

Electrical inductance in serial and parallel connected inductors.

### Electrical Parallel Circuits

Resistance, voltage and current in electrical parallel circuits.

### Electrical Series Circuits

Voltage and current in electrical series circuits.

Specific gravity and charge of lead acid batteries - temperature and efficiency.

### Resistors - Color Codes Calculator

Color codes for fixed resistors - values and tolerances - online calculator.

### Resistors - Letters and Digit Codes

Letter and digit codes to indicating resistor values.

### Resistors - Standard Values

Preferred number series for resistors.

### Voltage Dividers - Online Calculator

Output voltage potential divider.

## Search Engineering ToolBox

• the most efficient way to navigate the Engineering ToolBox!

## SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!