Resistors Notes
Resistors
Definition: Resistors are electrical components that oppose the flow of electric current, leading to voltage drops in circuits.
Resistor Colour Code
Purpose: Use the colour code to identify the value, tolerance, and multiplier of resistors.
Resistor Colour Table:
Colour | Digit | Multiplier | Tolerance |
|---|---|---|---|
Black | 0 | 1 | |
Brown | 1 | 10 | ±1% |
Red | 2 | 100 | ±2% |
Orange | 3 | 1000 | |
Yellow | 4 | 10,000 | |
Green | 5 | 100,000 | ±0.5% |
Blue | 6 | 1,000,000 | ±0.25% |
Violet | 7 | 10,000,000 | ±0.1% |
Grey | 8 | ±0.05% | |
White | 9 | ||
Gold | 0.1 | ±5% | |
Silver | 0.01 | ±10% |
How to Read Resistors
Four Band Resistor:
First two bands represent significant digits.
Third band is the multiplier (for value).
Fourth band indicates tolerance.
Five Band Resistor:
First three bands give significant digits.
Fourth band is the multiplier.
Fifth band gives tolerance.
Resistors in Series
Definition: Resistors connected in a single path, meaning the same current flows through each.
Characteristics:
Total current (Itotal) remains the same: [ I{total} = I1 = I2 = I3 = … = I_N ]
Total resistance (Rtotal) is the sum of individual resistances:
[ R{total} = R1 + R2 + R3 + … + R_N ]Total voltage (Vtotal) is the sum of potential drops:
[ V{total} = V1 + V2 + V3 + … + V_N ]
Example: For resistors with values 100Ω, 300Ω, and 50Ω:
[ R_{total} = 100 + 300 + 50 = 450Ω ]
Voltage across a total of 9V results in [ I_{total} = \frac{9V}{450Ω} = 0.02A ]
Resistors in Parallel
Definition: Resistors connected across the same two nodes.
Characteristics:
Voltage across each resistor in parallel remains the same:
[ V{total} = V1 = V2 = V3 = … = V_N ]Total current (Itotal) is the sum of the currents through each resistor:
[ I{total} = I1 + I2 + I3 + … + I_N ]The reciprocal of the total resistance is the sum of the reciprocals of each resistance:
[ \frac{1}{R{total}} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} + … + \frac{1}{R_n} ]
Example: For resistors of 10kΩ, 2kΩ, and 1kΩ:
[ \frac{1}{R{total}} = \frac{1}{10000} + \frac{1}{2000} + \frac{1}{1000} \rightarrow R{total} = 625Ω ]
Current, Voltage, and Resistance
Current (I): Flow of electric charge (measured in Amperes, A):
[ I = \frac{q}{t} ] where [ q ] is charge in coulombs and [ t ] is time in seconds.
Voltage (V): Potential difference driving current: [ V = I \times R ] (Ohm's Law).
Resistance (R): Opposition to flow of current: [ R = \frac{V}{I} ] (measured in Ohms, Ω).
Ohm's Law
Definition: States the relationship between voltage, current, and resistance.
Basic Formulas:
[ V = I \times R ]
[ I = \frac{V}{R} ]
[ R = \frac{V}{I} ]
Applications: Used to calculate any one of these three quantities when the others are known.
Electrical Power
Definition: Rate at which energy is transferred or converted.
Power equation:
[ P = V \times I ] (measured in Watts, W).
Conclusion
Understanding resistors' function, how to calculate their values in circuits, and their relationship with voltage, current, and resistance is crucial for mastering basic electrical principles. Resistive circuits form the foundation for more complex electrical studies and applications.