Lesson: Chapter - 14

Resistance

Some materials conduct current better than others. If we had a copper wire and a glass wire with the same length and cross section, and put the same potential difference across them, the current in the copper wire would be much larger than the current in the glass wire. The structure of copper, a conductor, is such that it permits electrons to move about more freely than glass, an insulator. We say that the glass wire has a higher resistance, R, than the copper wire.

Video Lesson - What is a Resistor

We can express resistance in terms of the potential difference, V, and the current, I:

R = ?V/I

Generally, the ? is omitted. For a given voltage, the larger the current, the smaller the resistance. The unit of resistance is the ohm (O). One ohm is equal to one volt per ampere: 1 O = 1 V/A.

Ohm’s Law

Ohm’s Law relates the three important quantities of current, voltage, and resistance:

I = V/R

This equation tells us that we can maximize the current by having a large voltage drop and a small resistance. This is one of the most important equations dealing with electromagnetism, and Physics is bound to call upon you to remember it.

Video Lesson - Ohm's Law Explained

Example

Three batteries are added to a circuit, multiplying the potential difference in the circuit by four. A resistor is also added, doubling the resistance of the circuit. How is the current in the wire affected?

Taking the initial voltage to be V and the initial resistance to be R, the initial current is I_i = V/R. The new voltage is 4V and the new resistance is 2R, so the final current is:

These changes double the current.

Resistivity

Resistivity, ?, is a property of a material that affects its resistance. The higher the resistivity, the higher the resistance. Resistance also depends on the dimensions of the wire—on its length, L, and cross-sectional area,A:

A longer wire provides more resistance because the charges have farther to go. A larger cross-sectional area reduces the resistance because it is easier for the charges to move. The unit of resistivity is the ohm-meter, O · m. The resistivity of copper is about 10^–8 O · m and the resistivity of glass is about 10¹² O · m. At higher temperatures, the resistivity of most metals increases.

Example

A copper wire of length 4 m and cross-sectional area 4 mm² is connected to a battery with a potential difference of 9 V. What is the current that runs through the wire? Approximate the resistivity for copper to be 10^–8 O · m.

As we know, the current in a wire is a measure of voltage divided by resistance. We know that the voltage for the circuit is 9 V, but we don’t know the resistance. However, since we know that the resistivity for copper is 10^–8 O · m, we can use the formula for resistivity to calculate the resistance in the wire.

First, we need to remember that area is measured in m², not mm². If 1 mm = 1 × 10^-3 m, then 4 mm² = 4 × (10^-3 m)² = 4 × 1-^-6 m².

Now we can plug the values for the resistivity of copper and the length and cross-sectional area of the wire into the equation for resistivity:

Once we know the resistance of the circuit, calculating the current involves a simple application of Ohm’s Law:

Conductivity

Infrequently, you may come across talk of conductivity and conductance rather than resistivity and resistance. As the names suggest, these are just the inverse of their resistant counterparts. Saying a material has high conductivity is another way of saying that material has a low resistivity. Similarly, a circuit with high conductance has low resistance. Someone with half a sense of humor named the unit of conductance the mho (), where 1 = 1 O¹.

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