Relationship between the Resistance and Dimensions of a Conductor

With a uniform wire/conductor of a given material and a given length, the resistance obtained by dividing Potential difference between any 2 points by Current is directly proportional to the distance between them. That is to say if the distance between the 2 points (on the conductor) increases the resistance also increases.

If 2 resistors each having resistance R ohms are connected in parallel the equivalent resistance Re is given by Product / Sum (Product over Sum)

Re = R*R/R+R
Re = R*R/2R
Re = R/2
Re = (1/2)*R
Each resistor will offer half of its resistance.

See the working in the slide. Click the previous button then after click on the slide screen.

Therefore, if two wires of the same material, having the same length and diameter are connected in parallel their resistance is half that of one wire. The effect of connecting two wires in parallel is similar to doubling the area of conductor. Connecting 7 wires in parallel is the same as increasing the cross section area of a wire 7 times and this reduces the resistance to a 1/7 (seventh) of one wire. Generally, the resistance of a given length of a conductor is inversely proportional to the cross section area. 


Other factors that influence resistance are; nature of the material (different materials have different resistances) and temperature (the resistance of some materials increase with an increase in temperature). So everything we have discussed above is true if temperature is constant.

Resistance of a wire = (Length of wire (L)/Cross Sectional Area (A))*a constant for a given material (ρ)

See the equation in the slide.

The constant of a material is called Resistivity of a material and it is represented by a Greek symbol rho (ρ). Resistivity is measured in ohm meter (Ωm)

Definition for Resistivity

This is the resistance of the specimen having one meter long and one meter square of cross sectional area.

Calculating Current in Two Parallel Resistances

Like I have already stated in one of the previous posts, voltage is the same in parallel resistor connection.
Voltage for resistor 1 = Voltage for resistor 2

That is to say (Voltage supplied), V = (I1R1 = I2R2).
Not forgetting that V = IR
Also Is = I1 + I2. (Is is the current supplied)
I-I1 = I1-I1+I2
I2 = I-I1
Substitute I2 in the equation V = (I1R1 = I2R2)
I1R1 = R2(I-I1)
I1R1 = IR2 - I1R2
I1R1 + I1R2 = IR2
I1(R1+R2) = I*R2
I1 = I*R2 / R1+R2
Similarly
I2 = I*R1 / R1+R2

Wiring a Three Pin Plug

Wiring a three pin Plug

Three Pin Plugs (or 3-pin plugs) are designed to protect the electrical appliance and its user from electrical hazards. They vary in size; there are those whose pins are moderately sized, also known as UK plugs, and those with large pins known as non-UK plugs. Someday or today you might need to change the 3-pin plug of your electrical appliance for some varying reasons. Though some electrical appliances are manufactured with the 3-pin plug molded on the AC in put cable, you might still need to change it. Perhaps you bought your electrical appliance when the plug pins are larger than the socket outlets. You will need to cut off that plug and replace it with the suitable one. In this post we will look at how to wire a three pin plug.

To wire a 3-pin plug, one has to be familiar with the colour codes of the wires:

• the live wire is brown
• the neutral wire is blue
• the earth wire is green and yellow striped

If you can get a new Universal 3-pin plug like the one in the picture below, unscrew the top cover of the plug, the 3 terminals and the cable grip.

Universal 3-pin Plug

Cut away about 1 cm of the insulation from each wire using a cable insulation stripper or a razor blade if the former is not in your possession. Make sure not to sever the wire strands.

Put the flex under the cord grip and screw it tightly in order to hold it in place.
Note: Do not leave the flex outside the plug to prevent the wire strands from breaking off their respective terminals as a result of strain.

Do not leave flex outside plug

Twist the wire strands so that there are no strands straying.

Connect the wires to their respective terminals. 3-pin plugs have their pins marked E for earth, N for neutral and L for live. Screw tightly all the terminals.

The connections should be like this.

Put back the cover and screw it tightly.
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