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Electrical Resistance in Serial and Parallel Networks

Resistors in parallel and serial connections.

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Serial Connection

series circuits

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

R = R 1 + 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

electrical parallel circuit

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

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

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

R = R 1 R2/ (R 1 + 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

I 1 = U / R 1 = (12 V) / (33 ohm) = 0.36 ampere

I2= U / R2= (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 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.

Voltage divider as Thevenin equivalent circuit

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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