# Solving Series Parallel Circuits Problems

The key to its solution lies in knowing the order in which the steps of the solution must be accomplished.Referring to the example combining series and parallel circuits and Figure 21.6, calculate \$I_3\$ in the following two different ways: (a) from the known values of \$I\$ and \$I_2\$ ; (b) using Ohm’s law for \$R_3\$ .The resistance R three is 13 ohms and we want to find out what is the current going through that resistor.

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Then we solve this for I three and we move this to the right hand side making it positive and then divide both sides by R three and we solve for I three.

So I three is V t minus I times R one over R three.

So I three is I minus I two which is 2.35 amps minus 1.61 amps which is 0.74 amps. So let's consider a loop where we begin here and traverse in this direction in which case we have a positive potential difference from the starting point to here across this EMF.

Then in part B, we're asked to solve the same question, what is I three by using a method involving Ohm's Law. So that's V t our terminal voltage I called it there, and then we're going in the same direction as the current across this resistor and so this is a drop in potential. Then we're going to go along this branch across R three again in the direction of the current.

This current produces a voltage drop of 36 volts across the 30-ohm resistor.

(Notice that the voltage drops across the 20- and 30-ohm resistors are the same.) The two branch currents of 1.8 and 1.2 amps combine at junction B and the total current of 3 amps flows back to the source.

The action of the circuit has been completely described with the exception of power consumed, which could be described using the values previously computed.

It should be pointed out that the combination circuit is not difficult to solve.

A circuit of this type is referred to as a COMBINATION CIRCUIT.

Solving for the quantities and elements in a combination circuit is simply a matter of applying the laws and rules discussed up to this point.

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