Before heading over to understanding the formula for electric resistance, let us try to understand the meaning of electric resistance and what exactly is its essence in a circuit. So electrical resistance is the opposite or the resistance offered by a circuit to free passage of current. Resistance exacts like friction in a circuit. Like friction opposes the free and easy motion, electrical resistance resists the flow of current through a wire.
There are basically two methods of finding the electrical resistance of a circuit. One is the conventional formula for electric resistance.
In the formula given above, p is rho which signifies the resistivity of a material. L is the length of the conductor given to you and a is the area of the cross-section of the wire or conductor given to you. This is the basic formula to find the electrical resistance of any given conductor.
Another formula using which you can determine the electrical resistance of a given system is by using Ohm's law. Ohm’s law is one of the most famous practical laws of circuital physics. Ohm’s law states that the current flowing through a circuit is directly proportional to the voltage applied across it and inversely proportional to the resistance offered by the wire, provided that the temperature remains constant. The formula for ohm's law is
Here V signifies the applied voltage
I represents the current
R is the electrical resistance
From the formula given above, we can find the electrical resistance if the voltage and the current are known to us.
1. What factors does the electrical resistance depend on?
The electrical resistance depends on several factors. These factors which alter the electrical resistance are given below
The Nature of The Material: The formula for electric resistance depends on the resistivity of the conducting material. The resistivity is a natural property of a material. It varies from material to material. Hence, the nature of the conductive material affects resistance
The Length of The Conductor: According to the formula for electrical resistance, the resistance of a material is directly proportional to the length of the conductor.
The Area of Cross-section: The area of cross-section is inversely proportional to electrical resistance.
The Temperature of The Conductor: The temperature is the final factor that alters the resistance of the conductor. Higher is the temperature, the lower is the resistance.
2. What is resistivity and what's its range for different materials?
Resistivity is a natural property of a conductor. Just like any other natural property we've studied, for instance, ductility, luster, brittleness, and other such physical properties, electrical resistivity is another property that varies from material to material. The electrical resistivity for different materials is given below
1.00 × 10-⁸
2.82 × 10-⁸
1.68 × 10-⁸
1.00 × 10¹⁴
2.30 × 10¹⁶
1.00 × 10²³
As we see, the resistivity is high for inductors such as wood, Teflon, and air whereas the conductivity is very low for good conductors of electricity such as silver, aluminum, and copper.
3. What is the dimensional formula for electric resistance?
The dimensional formula of electrical resistance is given below
R = V/ I
Where R is voltage and I is current.
Voltage = Force/ Charge × distance
The dimensional formula of force = M¹ L¹T-²
The dimensional formula for charge is = current × time = I¹T¹
∴ The dimensional formula of voltage = [Force × Charge-¹] × Distance
= [M¹ L¹ T-²] × [I¹ T¹]-¹ × [L¹] = [M¹ L² T-³ I-¹] . . . . (2)
From equation 2 and 1 we get
Resistance (R) = Voltage × Current-1
or, R = [M¹ L²T-³I-¹] × [I]-¹ = [M¹ L² T-³ I-²]
Therefore, the dimensional formula for resistance is written as ML²T-³I-².