# Analyzing Simple Circuits

## Analyzing a Series Circuit:

1. Find the equivalent (total) resistance, Rtotal, by adding all the individual resistances in the circuit.
2. Find the current in the circuit using Ohm's Law: I = V/Rtotal.
3. Find the voltage across each individual resistance using Ohm's Law: V = IR.
4. Check to be sure that the sum of all the voltage drops across the individual resistances equals the source voltage.

## Analyzing a Parallel Circuit:

1. If any parallel branch contains more than one resistance, find the equivalent (total) resistance in that branch by adding the individual resistances.
2. Find the current through each parallel branch using Ohm's Law: I = V/Rbranch.
3. Find the current through the voltage source by adding all the currents through the individual branches.
4. If any parallel branch contains more than one resistance, find the voltage drop across each resistance using Ohm's Law: V = IR.

## Analyzing a Compound Circuit:

1. If any parallel branch contains more than one resistance, find the equivalent (total) resistance in that branch by adding the individual resistances.
2. Replace each set of parallel branches in the circuit with a single equivalent (total) resistance.
1. If the resistances in each branch are equal, then the equivalent resistance is half of one of the branch resistances.
2. If the resistances in each branch are not equal, then
1/Requiv = 1/R1 + 1/R2 or Requiv = (R1R2) /(R1 + R2).
3. Find the equivalent (total) resistance, Rtotal, in the circuit by adding all of the series and equivalent resistances.
4. Find the current through the voltage source using Ohm's Law: I = V/Rtotal.
5. Find the current through each parallel branch.
1. If the resistances in each branch are equal, then the current through each branch is one-half the current in the series part of the circuit.
2. If the resistances in each branch are not equal, then find the current through each branch using Ohm's Law: I = V/R.
6. Find the voltage across each individual resistance and parallel branch using Ohm's Law: V = IR.
7. Check to be sure that the sum of all the voltage drops across the individual series resistances and parallel branches equals the source voltage.
8. Check to be sure that the sum of the currents through each parallel branch equals the voltage source current.

last update April 13, 2008 by JL Stanbrough