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Combined Series and Parallel Resistor Circuits

You frequently find both series and parallel connections in a single circuit. Circuits of this kind are sometimes referred to as combined or mixed circuits. It is possible, for example, to connect three resistors both in series or parallel connection or also in combined circuits as shown in the following graphic.

Resistor Circuits !

For the calculation of the total resistance R of the circuit a) you first determine the total resistance R1||2 of the two resistors R1 and R2 connected in parallel. Then the total resistance R of the series connection of R1||2 and R3 is determined. On the basis of Ohm's law and provided you know the supply voltage U you can then determine the current I3 and thus the voltage U3. The voltage U12 then emerges as the difference between U and U3; the currents I1 and I2 follow accordingly from Ohm's law.

Example: assuming that U = 10 V, R1 = 10 W, R2 = 40 W and R3 = 12 W, then the result for the total resistance is

Resistor Circuits !

For the currents and the voltages the following is true:

Resistor Circuits !

For circuit b) you first determine the total resistance R2-3 of the resistors connected in series R2 and R3 and then the total resistance R from the parallel connection of R1 and R2-3.

Example: assuming that U = 10 V, R1 = 50 W, R2 = 10 W and R3 = 40 W, then we obtain a total resistance:

Resistor Circuits !

For the currents and voltages the following is then obtained 

Resistor Circuits !

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