Electrical Concepts - Resistance and Ohm's Law

Lesson Context

  • Focus on electrical concepts: resistance and Ohm's Law.

Key Concepts

  • Resistance

    • Measure of opposition to current flow in an electrical circuit.
    • Unit: Ohm (Ω), symbolized by the Greek letter omega (Ω).
    • Named after Georg Simon Ohm, who studied voltage, current, and resistance relationships.

  • Ohm's Law

    • States that the current $I$ through a conductor is directly proportional to the potential difference $V$ between its ends.
    • Formula:
      IextisproportionaltoVI ext{ is proportional to } V
    • Different forms of the law include:
    • V=IRV = IR (Voltage = Current x Resistance)
    • R=VIR = \frac{V}{I} (Resistance = Voltage / Current)

RESISTORS

  • Definition: An electrical component that limits or regulates the flow of electrical current in a circuit.
  • Color Code for Resistors:
    • Composed of several colored bands that indicate resistance value and tolerance.
  • Color Bands Explanation:
    • 1st Digit: Value of 1st significant figure.
    • 2nd Digit: Value of 2nd significant figure.
    • Multiplier: Power of ten multiplier.
    • Tolerance: Range of acceptable variation in resistance value.
Resistor Color Code Table
Color1st Dig.2nd Dig.MultiplierTolerance
Black00$ imes 1 $± 1%
Brown11$ imes 10 $± 1%
Red22$ imes 100 $± 2%
Orange33$ imes 1000 $± 3%
Yellow44$ imes 10^4 $± 4%
Green55$ imes 10^5 $± 0.5%
Blue66$ imes 10^6 $± 0.25%
Violet77$ imes 10^7 $± 0.1%
Grey88$ imes 10^8 $± 0.05%
White99$ imes 10^9 $± 5%
Gold--$ imes 10^{-1} $± 5%
Silver--$ imes 10^{-2} $±10%
Ohm's Law Application
  • Calculating Current (I):
    • Formula: I=VRI = \frac{V}{R}
    • Example with 80 V circuit: For a series circuit with resistors:
    • Total resistance $R = 10 ext{ Ω}$
    • I=80V10Ω=8extAI = \frac{80 V}{10 Ω} = 8 ext{ A}.
  • Calculating Voltage across Resistors:
    • Using the formula V=IRV = IR for each resistor:
    • If $I = 8 A$, for different resistors:
    • V<em>1=IR</em>1=8Aimes5Ω=40VV<em>1 = IR</em>1 = 8 A imes 5 Ω = 40 V
    • V<em>2=IR</em>2=8Aimes1Ω=8VV<em>2 = IR</em>2 = 8 A imes 1 Ω = 8 V
    • V<em>3=IR</em>3=8Aimes3Ω=24VV<em>3 = IR</em>3 = 8 A imes 3 Ω = 24 V
    • V<em>4=IR</em>4=8Aimes1Ω=8VV<em>4 = IR</em>4 = 8 A imes 1 Ω = 8 V
Example Problem
  • Given a circuit with the following resistances:
    • R<em>1=1extΩ,R</em>2=6extΩ,R3=12extΩR<em>1 = 1 ext{ Ω}, R</em>2 = 6 ext{ Ω}, R_3 = 12 ext{ Ω} with a voltage of 12 V:
    • Solve for currents through each resistor using I=VRI = \frac{V}{R}:
      • I<em>1=12.0VR</em>1=12.0AI<em>1 = \frac{12.0 V}{R</em>1} = 12.0 A
      • I<em>2=12.0VR</em>2=2.00AI<em>2 = \frac{12.0 V}{R</em>2} = 2.00 A
      • I<em>3=12.0VR</em>3=1.00AI<em>3 = \frac{12.0 V}{R</em>3} = 1.00 A
  • Total current:
    I<em>total=I</em>1+I<em>2+I</em>3=12.0A+2.00A+1.00A=15.0AI<em>{total} = I</em>1 + I<em>2 + I</em>3 = 12.0 A + 2.00 A + 1.00 A = 15.0 A
Mini Quiz (Sample Questions)
  1. Identify resistance from given color bands.
  2. Calculate current in a circuit given voltage and different resistances.
  3. Apply Ohm's Law to find voltage drop across resistors in series.
Practice Problems
  • Calculate the total current in circuits with different resistance values.