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)

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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

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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:

R₁ (ohms)

R₂(ohms)

R₃ (ohms)

R₄ (ohms )

R₅ (ohms)

Voltage (V)

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I₁ (amps)

I₂(amps)

I₃ (amps)

I₄ (amps)

I₅ (amps)

R (ohms)

I (amps)

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.