Resistance & Conductance

What is Resistance?

Electrical Resistance is the opposition to the flow of current. As we all know, voltage, current, and resistance are the three components that form Ohm’s law. The voltage behaves like a pushing force to move electric current around the circuit, while the resistance acts in the opposite direction to resist the flow of current. Resistance can be defined when an electric potential is applied at two points to produce a current flow in a conductor.

Resistance is measured in Ohm (Ω):

Resistor Color Code:

Considering the function of a resistor is to oppose current flow, we can use it to control the amounts that flow through different elements. Using resistors with specific resistance values will help us manage the current that flows in the circuit. Resistors have the same shape, but they come in different sizes and with colored stripes. The colored bands can be used to find the resistive value and tolerance. Although resistors come with this information, it is essential to understand how to determine their values.

The number and color of stripes on each resistor differ. The number of bands can range from 3 to 6, but the most commonly used ones are the 4-5 band resistors. The color codes help identify the resistance and tolerance using a color chart table. In a four-band resistor, the first two colors represent the two first digits. The third band represents the multiplier, while the clast one represents the tolerance. We read the resistance from the end with the most bands,cand the space between the last two bands also indicates the reading direction. In three, or five-band resistors, the last two stripes indicate tolerance and multiplier. However, you will only notice a difference in the number of digits. But in a six-band resistor, the end color represents the temperature coefficient.

Resistance and Resistivity:

As stated earlier, resistance is a measure of the object’s ability to oppose current flow. On the other hand, resistivity defines the property of the material by which it resists the amount of current that flows through it. Resistivity, denoted by ρ, solely depends on the nature of the material and temperature. However, resistance depends upon the below factors:

• Length
Resistance is proportional to the length of the conductor. If the conductor length increases, the resistance will also increase.
R ∝ L

• Cross-sectional area
Resistance is inversely proportional to the cross-sectional area. If the cross-sectional area of a wire is doubled, the resistance is halved.

R ∝ 1/A

• Material and Temperature
The type of material determines its resistivity and whether it is suitable for various electrical components. Moreover, resistivity varies with temperature.
Since
R ∝ L and R ∝ 1/A

Then,
R ∝ L/A

By inserting the resistivity constant (ρ) that varies based on the material;
R =pL/A (ohm)

Solving for ρ;
R = pL/A

AR = pL

p = AR/L

ρ is measured in ohmmeters (Ω m).

Typical values of resistivity measured at a room temperature are given below:

Example:

The resistance of a 6 m length of wire is 900 Ω. Determine (a) the resistance of a 4 m length of the same wire, and (b) the length of the same wire when the resistance is 120 Ω.

(a) R =? L= 4 m
Since,

R∝L
900 ∝ 6
900 = k (6)
where K is the proportionality coefficient

k = 900/6 = 150Ω

Therefore, when the length is 4m
R = K×L = (150) (4) = 600 Ω

(b) R = 120 Ω L=?
R = K×L
120 = (150) (L)
L = 0.8 m

Example:

A piece of wire of cross-sectional area 4 mm2 has a resistance of 600 Ω. Find (a) the resistance of a wire of the same length and material if the cross- sectional area is 10 mm2, (b) the cross-sectional area of a wire of the same length and material of resistance 950 Ω.

(a) R =? a = 10 mm²
Since,
R ∝ 1/A
600 ∝ 1/4

Finding the proportionality coefficient,
600 ∝ k/4
600 = k/4
k = 2400

Finding R,

R = k/a = 2400/10 = 240Ω

You can see that the resistance has decreased as the cross-sectional area increased.

(b) a=? R = 750 Ω

R = k/a
750 = 2400/a
a = 2400/750
a = 3.2 mm2

Conductance:

Conductance is the opposite of resistance in that it defines how easy it is for current to flow through a conductor. Mathematically, conductance is the reciprocal of resistance and is measured in Siemens (s). However, Siemens is sometimes referred to as mho (Ω−¹).

Conductance and conductivity:

A conductor is a material that allows current to flow easily due to its low resistance. However, conductance is the extent to which an object conducts electricity. On the other hand, conductivity is a measure of how easy it is for an electric charge to pass through a material. Since conductivity is the reciprocal of resistivity, some factors affect conductance.

Length:

Conductance and length are inversely proportional. If length increases, conductance decreases.

G = 1/L

The cross-sectional area:

Conductance and the cross-sectional area (of a conductor) are directly proportional. If the area increases, conductance increases too.

G ∝ A

Therefore,

G = A/L
G ∝ A/L

Now, a constant of conductivity is introduced. It is designated by the symbol sigma (Ϭ), which is again the reciprocal of resistivity (ρ).

Understanding conductivity helps us determine good and bad conductors for electricity. Just like resistivity, conductivity also depends on the material and a specified temperature. Metals like silver, aluminium, gold, and copper are classified as good conductors and are usually used for wires.

Example:

Calculate the conductance and conductivity of a copper wire of length 10m and cross-sectional area of 40mm². The resistance of the wire is 200Ω.