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 = 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
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 / 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:
Power Dissipated by a Resistor
The power dissipated by a resistor can be expressed as
P = U I
= R I^{2}
= U^{2} / R (4)
where
P = power (W, Js)
Thévenin Equivalent Circuit
Thévenin’s theorem states that
 any twoterminal 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.
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