Electrical Resistance: Difference between revisions

Revision as of 23:49, 1 December 2015

Electrical Resistance is the measure of how difficult it is for a current to pass through a conductor.

This quantity often measured in ohms [math]\displaystyle{ \Omega(\frac{Volts}{Amps}) }[/math] is used to determine the amount of current that will pass through a circuit. Resistance itself is dependent on a variety of factors including material, shape, and temperature. In most applications the resistance of a wire is assumed to be zero.

The Main Idea

State, in your own words, the main idea for this topic Electric Field of Capacitor

A Mathematical Model

Resistance is often expressed in the following form [math]\displaystyle{ R = \frac{\rho L}{A} }[/math] where R is the resistance [math]\displaystyle{ \rho }[/math] is the resistivity L is the length and A is the cross-sectional area.

In a circuit the Electrical Resistance is often calculated as [math]\displaystyle{ R = \frac{|\Delta V|}{I} }[/math] Often written [math]\displaystyle{ I = \frac{|\Delta V|}{R} }[/math] where V is the voltage and I is the current and R is the resistance. In these equations voltage and resistance are independent variables and Current is the dependant variable.

Water Analogy

Electrical Resistance in a particular material is often compared to a pipes of varying diameter. The larger the pipe the easier it is for water to get through. This is equivalent to lower resistance in electricity.

Resistivity of Materials

Every conductor has a natural resistivity that it relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivity.

Temperature

In addition to each material having a different resistivity. The same materials at different temperatures have different resistivities. As materials heat up it becomes harder and harder for current to pass through them. This is because at the sub-atomic level. The nuclei are moving faster making it harder for electrons to move through.

File:Temperature2.gif

Examples

3 examples of potential problems involving resistance.

Simple

Question

An unknown resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

Answer

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

Middling

Difficult

Connectedness

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History

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 In addition to each material having a different resistivity. The same materials at different temperatures have different resistivities. As materials heat up it becomes harder and harder for current to pass through them. This is because at the sub-atomic level. The nuclei are moving faster making it harder for electrons to move through.
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 ==Examples==