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# 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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