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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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)

I₁ (amps)

I₂ (amps)

I₃ (amps)

I₄ (amps)

I₅ (amps)

R (ohms)  

I (amps)

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm