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
    • Req(series)=R1+R2+R3+...+Rn=k=1nRk R_{eq(series)} = R_{1} + R_{2} + R_{3} + . . . + R_{n} = \sum_{k=1}^{n} R_{k}

    • 1Req(parallel)=1R1+1R2+1R3+...+1Rn=Rn=k=1nRk \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: Req(parallel)=11R1+1R2+1R3+...1Rn=1k=1n1Rk 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 (Ω\Omega ) and can be determined for a circuit by dividing the voltage by the current (in preview of Ohm’s law: V=IRV=IR).
  • When solving for resistance in series, we must use the summation equation:
    • Req(series)=R1+R2+R3+...+Rn=k=1nRk 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, Req(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:
    • 1Req(parallel)=1R1+1R2+1R3+...+1Rn=Rn=k=1nRk \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: Req(parallel)=11R1+1R2+1R3+...1Rn=1k=1n1Rk 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, Req(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

    Introduction to Waves
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Resistance

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