Resistance

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: $R_{eq(parallel)} = \frac{1} { \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + ... \frac{1}{R_{n}} } = \frac{1} { \sum_{k=1}^{n} \frac{1}{R_{k}} }$

• 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)