# Parallel Circuits

Parallel Circuits have multiple current paths

Removal of a circuit element may allow other branches of the circuit to continue operating

# Combination Series-Parallel Circuits

A circuit doesn't have to be completely serial or parallel

First, look for portions of the circuit with parallel elements.

Replace parallel resistors with an equivalent single resistor

Work back to original circuit using KCL and KVL until you know the current, voltage, and resistance of each individual circuit element

Often times will lead to systems of equations to solve

# Example 1: Two Voltage Sources

Find the current flowing through R3 if R3 has a value of 6 ohms. What is the power dissipated in R3?

# Batteries

A cell or battery (combination of cells) provides a potential difference, oftentimes referred to as an electromotive force or emf.

A battery can be thought of as a pump for charge, raising it from a lower potential to a higher potential

Ideal batteries have no resistance

In real batteries, the terminal voltage is slightly lower than the battery's emf

# Ideal Battery

# Real Battery