Resistance  Electric Circuits
Resistance
Lessons
Notes:
In this lesson, we will learn:
 A review on what is an electric circuit and the main components: battery (voltage), closed wire path (current), and devices/resistors that use up electricity (resistance).
 What is resistance?
 What is the difference between connecting your circuit in series vs. parallel configurations for resistors?
 What is a battery and how does it provide voltage for an electric circuit?
 How to solve resistance problems for both series and parallel circuits by using the summation equations for equivalent resistance in series and equivalent resistance in parallel
 $R_{eq(series)} = R_{1} + R_{2} + R_{3} + . . . + R_{n} = \sum_{k=1}^{n} R_{k}$
 $\frac{1} {R_{eq(parallel)}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + ... + \frac{1}{R_{n}} = R_{n} = \sum_{k=1}^{n} R_{k}$
 OR: $R_{eq(parallel)} = \frac{1} { \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + ... \frac{1}{R_{n}} } = \frac{1} { \sum_{k=1}^{n} \frac{1}{R_{k}} }$
Notes:
 Resistance is a property of the electronic device (resistor; or even battery and wires can have some resistance too and use up some voltage)
 It is a measure of how difficult it is for charges to travel through the circuit
 Resistors in a circuit represent electronic devices that use up voltage
 The greater the resistance, the bigger the voltage drop
 Resistances of metals are CONSTANT and INDEPENDENT of voltage
 The unit for resistance is the ohm ($\Omega$) and can be determined for a circuit by dividing the voltage by the current (in preview of Ohm’s law: $V=IR$).
 When solving for resistance in series, we must use the summation equation:
 $R_{eq(series)} = R_{1} + R_{2} + R_{3} + . . . + R_{n} = \sum_{k=1}^{n} R_{k}$
 Where all resistors in series are added up for the total resistance
 Thus, R_{eq(series)} is greater than any single RK independently; adding more resistors in series will increase the total resistance
 When solving for resistance in parallel, we must use the summation equation:
 $\frac{1} {R_{eq(parallel)}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + ... + \frac{1}{R_{n}} = R_{n} = \sum_{k=1}^{n} R_{k}$
 OR: $R_{eq(parallel)} = \frac{1} { \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + ... \frac{1}{R_{n}} } = \frac{1} { \sum_{k=1}^{n} \frac{1}{R_{k}} }$
 Where the total resistance is equal to the inverse of the sum of all inverses of resistors (branches) in parallel
 Thus, R_{eq(parallel)} is less than any single RK independently; adding more resistors in parallel will decrease the total resistance
 In terms of resistance, the advantage of a series configuration is that the battery will last longer; the greater the resistance, the more difficult it is for the charges to travel; thus, less charge is drawn out of the battery over time (less current)
 A parallel configuration generates lesser resistance, allowing charges to flow freely; thus, more charge is drawn out of the battery over time (more current)

Intro Lesson
Introduction to resistors and resistance:

3.
Solving for Resistors in BOTH Series & Parallel Configurations