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:
I ext{ is proportional to } V - Different forms of the law include:
- V = IR (Voltage = Current x Resistance)
- R = rac{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
| Color | 1st Dig. | 2nd Dig. | Multiplier | Tolerance |
|---|---|---|---|---|
| Black | 0 | 0 | $ imes 1 $ | ± 1% |
| Brown | 1 | 1 | $ imes 10 $ | ± 1% |
| Red | 2 | 2 | $ imes 100 $ | ± 2% |
| Orange | 3 | 3 | $ imes 1000 $ | ± 3% |
| Yellow | 4 | 4 | $ imes 10^4 $ | ± 4% |
| Green | 5 | 5 | $ imes 10^5 $ | ± 0.5% |
| Blue | 6 | 6 | $ imes 10^6 $ | ± 0.25% |
| Violet | 7 | 7 | $ imes 10^7 $ | ± 0.1% |
| Grey | 8 | 8 | $ imes 10^8 $ | ± 0.05% |
| White | 9 | 9 | $ imes 10^9 $ | ± 5% |
| Gold | - | - | $ imes 10^{-1} $ | ± 5% |
| Silver | - | - | $ imes 10^{-2} $ | ±10% |
Ohm's Law Application
- Calculating Current (I):
- Formula: I = rac{V}{R}
- Example with 80 V circuit: For a series circuit with resistors:
- Total resistance $R = 10 ext{ Ω}$
- I = rac{80 V}{10 Ω} = 8 ext{ A} .
- Calculating Voltage across Resistors:
- Using the formula V = IR for each resistor:
- If $I = 8 A$, for different resistors:
- V1 = IR1 = 8 A imes 5 Ω = 40 V
- V2 = IR2 = 8 A imes 1 Ω = 8 V
- V3 = IR3 = 8 A imes 3 Ω = 24 V
- V4 = IR4 = 8 A imes 1 Ω = 8 V
Example Problem
- Given a circuit with the following resistances:
- R1 = 1 ext{ Ω}, R2 = 6 ext{ Ω}, R_3 = 12 ext{ Ω} with a voltage of 12 V:
- Solve for currents through each resistor using I = rac{V}{R} :
- I1 = rac{12.0 V}{R1} = 12.0 A
- I2 = rac{12.0 V}{R2} = 2.00 A
- I3 = rac{12.0 V}{R3} = 1.00 A
- Total current:
I{total} = I1 + I2 + I3 = 12.0 A + 2.00 A + 1.00 A = 15.0 A
Mini Quiz (Sample Questions)
- Identify resistance from given color bands.
- Calculate current in a circuit given voltage and different resistances.
- Apply Ohm's Law to find voltage drop across resistors in series.
Practice Problems
- Calculate the total current in circuits with different resistance values.