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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.

For the calculation of the total resistance *R* of the circuit a) you first determine the total resistance *R*_{1||2} of the two resistors *R*_{1} and *R*2 connected in parallel. Then the total resistance *R* of the series connection of *R*_{1||2} and *R*_{3} is determined. On the basis of Ohm's law and provided you know the supply voltage *U* you can then determine the current *I*_{3} and thus the voltage *U*_{3}. The voltage *U*_{12} then emerges as the difference between *U* and *U*_{3}; the currents *I*_{1} and *I*_{2} follow accordingly from Ohm's law.

**Example:** assuming that *U* = 10 V, *R*_{1} = 10 W, *R*_{2} = 40 W and *R*_{3} = 12 W, then the result for the total resistance is

For the currents and the voltages the following is true:

For circuit b) you first determine the total resistance *R*_{2-3} of the resistors connected in series *R*_{2} and *R*_{3} and then the total resistance *R* from the parallel connection of *R*_{1} and *R*_{2-3}.

**Example:** assuming that *U* = 10 V, *R*_{1} = 50 W, *R*_{2} = 10 W and *R*_{3} = 40 W, then we obtain a total resistance:

For the currents and voltages the following is then obtained