Resistance is the opposition to the flow of electric current in a conductor. It is measured in ohms (Ω) and is determined by the material, length, and cross-sectional area of the conductor. The formula for resistance is:

**Formula:** *R = ρ (L / A)*

**R:**Resistance (ohms, Ω)**ρ:**Resistivity of the material (ohm-meters, Ω·m)**L:**Length of the conductor (meters, m)**A:**Cross-sectional area of the conductor (square meters, m²)

In DC circuits, resistance determines the amount of current that flows for a given voltage, as described by Ohm's Law:

**Formula:** *I = V / R*

**I:**Current (amperes, A)**V:**Voltage (volts, V)**R:**Resistance (ohms, Ω)

**Example Calculation:**

**Task:**Calculate the current in a DC circuit with a voltage of 24 V and a resistance of 8 Ω.**Solution:**Use the formula*I = V / R*.-
*I = 24 V / 8 Ω = 3 A*

The equivalent resistance (R_{eq}) in a parallel circuit is the reciprocal of the sum of the reciprocals of the individual resistances (R_{1}, R_{2}, R_{3}, ..., R_{n}) of all components connected in parallel.

1 / R_{eq} = 1 / R_{1} + 1 / R_{2} + 1 / R_{3} + ... + 1 / R_{n}

**R**: The equivalent resistance of the parallel circuit._{eq}**R**: The individual resistances of each component in the parallel circuit._{1}, R_{2}, R_{3}, ..., R_{n}

In a parallel circuit, each component has the same voltage applied across it, and the total current is the sum of the currents through each component. The reciprocal of the equivalent resistance is calculated by adding the reciprocals of the individual resistances, representing how current divides and flows through parallel branches.

The formula 1 / R_{eq} = 1 / R_{1} + 1 / R_{2} + 1 / R_{3} + ... + 1 / R_{n} mathematically expresses this concept, where each 1 / R_{i} is the reciprocal of the resistance of a specific component in the parallel circuit.

The equivalent resistance (R_{eq}) in a series circuit is the sum of the individual resistances (R_{1}, R_{2}, R_{3}, ..., R_{n}) of all components connected in series.

R_{eq} = R_{1} + R_{2} + R_{3} + ... + R_{n}

**R**: The equivalent resistance of the series circuit._{eq}**R**: The individual resistances of each component in the series circuit._{1}, R_{2}, R_{3}, ..., R_{n}

In a series circuit, the current flows through each component one after another, so the total resistance experienced by the current is the sum of all resistances in the circuit. This can be understood by examining how resistances add up in a linear path, contributing to the overall resistance encountered by the current.

The formula R_{eq} = R_{1} + R_{2} + R_{3} + ... + R_{n} mathematically represents this concept, where each R_{i} is the resistance of a specific component in the series.

In AC circuits, resistance works alongside reactance to form impedance. The total impedance (Z) is given by:

**Formula:** *Z = √(R² + X²)*

**Z:**Impedance (ohms, Ω)**R:**Resistance (ohms, Ω)**X:**Reactance (ohms, Ω)

**Example Calculation:**

**Task:**Calculate the impedance of an AC circuit with a resistance of 10 Ω and a reactance of 15 Ω.**Solution:**Use the formula*Z = √(R² + X²)*.-
*Z = √(10 Ω)² + (15 Ω)² ≈ 18.03 Ω*

In three-phase systems, resistance calculations are crucial for determining power loss and efficiency. For balanced loads, the total power (P) in a three-phase system is given by:

**P:**Power (watts, W)**V**Line voltage (volts, V)_{line}:**I**Line current (amperes, A)_{line}:**V**Phase voltage (volts, V)_{phase}:**I**Phase current (amperes, A)_{phase}:**cos(ϕ):**Power factor (dimensionless)

**Example Calculation for Star Connection:**

**Task:**Calculate the power in a three-phase star-connected system with a line voltage of 400 V, a line current of 20 A, and a power factor of 0.8.**Solution:**Use the formula*P = √3 × V*._{line}× I_{line}× cos(ϕ)-
*P = √3 × 400 V × 20 A × 0.8 ≈ 11,090 W*

**Example Calculation for Delta Connection:**

**Task:**Calculate the power in a three-phase delta-connected system with a phase voltage of 230 V, a phase current of 15 A, and a power factor of 0.9.**Solution:**Use the formula*P = 3 × V*._{phase}× I_{phase}× cos(ϕ)-
*P = 3 × 230 V × 15 A × 0.9 ≈ 9,315 W*

Resistors are components used to limit the flow of current in an electrical circuit. They are color-coded to indicate their resistance values. Here’s a guide to understanding these color codes:

The color bands on a resistor represent numbers and multipliers. Here is the color-to-number mapping:

**Black**: 0**Brown**: 1**Red**: 2**Orange**: 3**Yellow**: 4**Green**: 5**Blue**: 6**Violet**: 7**Gray**: 8**White**: 9

Most resistors have four color bands, each representing a different aspect of the resistor’s value:

**Band 1**: First significant digit**Band 2**: Second significant digit**Band 3**: Multiplier (the number of zeros to add)**Band 4**: Tolerance (the acceptable range of deviation from the nominal value)

If a resistor has the color bands Red, Green, Brown, and Gold, it translates to:

**Red**(2)**Green**(5)**Brown**(x10)**Gold**(±5% tolerance)

So, the resistor value is 25 × 10 = 250 Ω with a tolerance of ±5%.

Below is a table that provides a 4 wire color code for identifying resistors. Use the button below to show or hide the table.