### Resistors in Series and Parallel

Resistors can be connected in series connection alone or in parallel connection alone. Some resistor circuits are made from combination of series and parallel networks to develop more complex circuits. These circuits are generally known as Mixed Resistor Circuits. Even though these circuits have combined series and parallel circuits, there is no change in the method of calculating the Equivalent Resistance. The basic rules of individual networks like “same current flows through resistors in series” and “voltage across resistors in parallel is same” are applicable to mixed circuits.

An example of mixed resistors circuit is shown below

Though they look complicated, the mixed resistor circuits can be reduced to a simple circuit consisting of only one voltage source and a single resistor by following the simple rules of resistors in series and resistors in parallel.

An example of mixed resistors circuit is shown below

It consists of four resistors R1, R2, R3 and R4 in a mixed resistor circuit combination. The supply voltage is V and the total current flowing in the circuit is I. The current flowing through the resistors R2 and R3 is I1 and the current flowing through the resistor R4 is I2.

Here the resistors R2 and R3 are in series combination. Hence applying the rule of resistors in series combination the equivalent resistance of R2 and R3 is given as

RA = R2 + R3

Here R_A is the equivalent resistance of R2 and R3

Now the resistors R2 and R3 can be replaced by a single resistor RA. The resulting circuit is shown below.

Now the resistors RA and R4 are in parallel combination. Hence by applying the rule of resistors in parallel combination the equivalent resistance of RA and R4 is

RB = RA × R4 / (RA + R4)

Here RB is the equivalent resistance of RA and R4

Now we can replace the resistors RA and R4 with a single resistor RB.After replacing the resistors the resulting circuit is shown below.

Now the circuit consists of only two resistors. Here also the resistors R1 and RB are in series combination. Hence by applying the rule of resistors in series the total circuit equivalent resistance is given as

REQ = R1 + RB

Here REQ is the total circuit equivalent resistance. Now the resistors R1 and RB can be replaced by a single resistor REQ.

The final equivalent circuit for above complex circuit is shown below.

The final equivalent circuit for above complex circuit is shown below.

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