Current & Resistance

Resistance Concepts

Resistance is a fundamental property of materials that opposes the flow of electric current. It is a key concept in understanding how electrical circuits function, especially in the context of Ohm's Law and circuit analysis.

• Definition: Resistance (R) is the measure of how much a material opposes the flow of electric current. It is measured in ohms (Ω).

• Ohm's Law: The relationship between voltage (V), current (I), and resistance (R) is given by the equation:

• Physical Factors: Resistance depends on the material, length, cross-sectional area, and temperature of the conductor.

• Resistor Symbol: The standard circuit symbol for a resistor is shown below.

Temperature Dependence of Resistance

The resistance of most conductors changes with temperature. This effect is particularly important in devices like light bulb filaments, where temperature variations are significant.

• Temperature Coefficient: For many metals, resistance increases with temperature. The relationship is approximately linear over moderate temperature ranges and is given by: where is the resistance at reference temperature , is the temperature coefficient of resistance, and is the final temperature.

• Applications: This property is used in temperature sensors and must be considered in circuit design, especially for high-power devices.

• Example: The filament of a light bulb has a much higher resistance when hot than when cold, affecting the current drawn when the bulb is first turned on.

Resistor Series

When resistors are connected end-to-end in a circuit, they are said to be in series. The total resistance of resistors in series is the sum of their individual resistances.

• Series Connection: In a series circuit, the same current flows through each resistor, but the voltage across each may differ.

• Total Resistance: The equivalent resistance for resistors in series is:

• Circuit Symbol: The diagram below shows multiple resistors connected in series.

• Example: If three resistors of 2 Ω, 3 Ω, and 5 Ω are connected in series, the total resistance is 10 Ω.

Additional info:

• Ohm’s 2nd Law (not explicitly defined in the notes) often refers to the relationship between resistivity, length, and cross-sectional area: , where is resistivity, is length, and is area.

• When a wire is melted and recast to double its length, its resistance increases by a factor of four (since for constant volume).