Resistors in series and parallel

Resistors in series

To implement a circuit with resistors in series you have to connect one resistor after the other one. (see the picture).

The equivalent resistor value of the resistors connected in series is equal to the addition of all resistor´s value.

On this case, the current flowing through all resistors is the same. Then:

RTS (series equivalente resistor value) = R1+R2+R3

The current value in the equivalent circuit (see the picture) can be calculated using the Ohm's law. (I = V/R)

This current is the same as the current on the original circuit

Once you have the current that flows through the circuit, you can get the voltage across each of the resistors in the original circuit using the Ohm's law.

- Voltage on R1 is V1 = I x R1
- Voltage on R2 is V2 = I x R2
- Voltage on R3 is V3 = x I R3

Resistors in parallel

On the series resistor circuit the current has only one path to travel through.

In a parallel resistor circuit the current is divided in several paths.

We can connect 2 or more resistors in parallel. These resistors are joined as shown in the picture.

The current supplied by the voltage source is the same on the original circuit (with R1, R2 and R3) and on the equivalent one.

On the original circuit the current is divided among the resistors and the current value on each of them depends on each resistor`s value. I = V/R (Ohm`s Law). Where R can be R1, R2 or R3.

Remember that the addition of all the currents is always the same.

The equivalent resistor value of a parallel circuit is: (for a 3 resistor circuit)

RTP (total parallel resistor value) = 1/(1/R1 + 1/R2 + 1/R3)

Showing the same formula in a slightly different way, we get

1/RTP = 1/R1 + 1/R2 + 1/R3

If we use the conductance formula G = 1/R. (The conductance is the inverse of the resistance and its unit is the Mho or Siemens), we can rewrite the above formula to obtain:

GTP = G1 + G2 + G3.
The equivalent conductance is the addition of conductances or

GTP = 1/R1 + 1/R2 + 1/R3.
The equivalent conductance is the addition of the inverse resistors value (resistance):

As we may allready know the total conductance is the inverse of the total resistance GTP = 1/RTP.

Clearing the last formula for RTP, we obtain RTP = 1/GTP wich is the equivalent resistor value of a set of resistors in parallel.

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