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# Electrical Resistance in Serial and Parallel Networks

## Resistors in parallel and serial connections

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

R = R1 + R2 + .... + Rn                   (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 / R1 + 1 / R2 + .... + 1 / Rn                  (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) I1 (amps)

R2 (ohms) I2 (amps)

R3 (ohms) I3 (amps)

R4 (ohms) I4 (amps)

R5 (ohms) I5 (amps)

Voltage (V)

R (ohms)   I (amps)

## Related Topics

• Electrical - Electrical units, amps and electrical wiring, wire gauge and AWG, electrical formulas and motors

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## Citation

• Engineering ToolBox, (2014). Electrical Resistance in Serial and Parallel Networks. [online] Available at: https://www.engineeringtoolbox.com/resistance-serial-parallel-connections-d_1881.html [Accessed Day Mo. Year].

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