Relation Between Power and Resistance

A way of visualizing the power and resistance relation is to think of a constant voltage source or a battery. When there's a large resistance across the circuit, very little current can flow so very little power is being offered by the battery and the resistor would not get too warm because there's less power. However, if you reduce the resistance more current will flow and the resistor will get warmer because we have increased the power.

So, wherever there is power, surely there will be resistance. It means that both are essential factors not only in Physics but also in our real lives.

Power Resistance Relation

The relationship between Power and Resistance can be expressed in two following ways:

1. \[P = \frac{V^2}{R} \]

Where,

P is the Power and we measure it in watts or W. 

R is the resistance measured in ohms (Ω).

V = the potential difference applied across the ends of the conductor and is measured in Volts or simply V.

2. The second way to express the power resistance relationship is by using the following power and resistance equation:

\[ P = I^{2} R \]

Where I is the electric current measured in Ampere or A.

What is work?

Work is done when some force is applied to the object and it gets displaced in the direction of motion. The work done on an object by a force is equal to the product of the magnitude of the force and the distance moved by an object in the direction of the force. Work has no direction but only magnitude. Hence, it is a scalar quantity.

Work Formula

The work done by a force is defined as the product of the cos component of a force and the displacement of an object in the direction of the force. The formula is given as (F cos theta) d or F.d. From this, we can understand that if there is no displacement, then there is no work done irrespective of the force applied to the object. There is no work done if,

• The force is zero

• The displacement is zero

• The force and displacement are mutually perpendicular to each other.

Unit of work

The SI unit of work is Joule (J). One joule is defined as one unit of force applied on an object to move it for one meter. 1 Joule= 1 Newton * 1 metre. Let us see an example of work done.

If a force of 10 Newton is applied to an object to move it for 2 metres, then the work done is 20 joules.

What is Power?

Power is a physical concept that has different meanings. Its definition depends on the context and available information. 

We define power as the ability of the body to do work in a unit of time. For example, person A does 30 J of work in 2 hrs and another person B does the same amount of work in 3 hrs, so here if we use the following formula:

Power  = Work / time

Case 1: 30/2 = 15 W

Case 2: 30/3 = 10 W

We can see that the capacity of person A is more than person B. So, power A is greater than the power of B.

However, in electrical terms, power is defined as the product of the current and the voltage.

P = VI

Where,

V is the potential difference and it is measured in volts.

I is measured in Ampere.

Unit of Power

Power is a scalar quantity as it only has magnitude and no direction. The SI unit of power is Joules per second which is termed, Watts. One watt is defined as the power required to do one joule of work in one second. The unit Watt is named in honour of Sir James Watt, the one who developed the steam engine. 

What is Resistance?

While driving a car at high-speed, we must slow down our car some distance before the speed breakers, otherwise, our car will jump with a great amount of jerk. So, here, our high-speed car is the maximum current that is flowing through the circuit (road) and the speed breaker is the resistance to avoid accidents or short circuits in our homes.

So, resistance is the obstruction connected across the circuit to avoid the overflow of charge through the circuit. It is measured in Ohms, where we symbolize it with omega or Ω.

According to Ohm's Law, we can represent resistance as voltage/current. As per this law, Resistance is constant and independent of the current. It is further written as R= ⍴ L/A, where l is the length, A is the area and rho is resistivity.

This shows that resistance is directly proportional to the length and inversely proportional to the area. Here, resistivity is measured in ohm meter, length in meter, and area in meter squares.

Applications of Ohm's Law in Daily Life 

• We can regulate the speed of the fan using a regulator. The current flowing through the fan can be regulated by controlling the resistance via a regulator. We can calculate current, resistance, and power using Ohm's law of any input added to the appliances. 

• The electric heaters consist of high resistance coils that generate the required amount of heat by obstructing the flow of current. This law can help to determine the power of these heaters. 

• We can determine the input of power for electric kettle and iron to produce a sufficient amount of heat. 

Factors Affecting Resistance 

The electric resistance of a conductor can be affected by the following factors.

• Length of the conductor

• The cross-sectional area of the conductor.

• The temperature of the conducting material

• Conductor's material 

Power and Resistance Formula

We noticed that the formulas mentioned above describe the relation between power and resistance. Consider the following equation:

\[ P = I^{2}{R} \]

Here, we can see that the electric power is directly proportional to resistance on keeping I constant.

From this, we infer the following things:

• When power increases, the resistance also increases, while keeping current I constant.

• However, when the resistance in the circuit decreases, power in the circuit also decreases, while keeping current I constant.

Now, consider another following equation:

\[ P = \frac{V^{2}}{R} \]

From here, we can see that the power P is inversely proportional to the resistance R. 

From this, we can infer the following things:

For any constant Potential difference

• When the power in the circuit is high, resistance will be lesser.

• However, if the power is low, the resistance will be high.

Power Resistance Formula

Deriving the Power and Resistance formula will help us in understanding the concept of the power and resistance relation.

In physics, power and resistance can be related using two formulas, which we will discuss in this article in detail.

We know that the electric power or P is the measure of the electric current I with q coulombs of charge passing through a potential difference of V (in volts) in time t seconds. Mathematically, we can express this statement as:

P = Vq/t = VI…..(1)

We know that Ohm’s law is stated as: 

V = IR

Where V is directly proportional to the current.

Now, applying this law in equation (1), we get:

\[ P = I \times IR = I^{2} R \]

Also, 

\[ I = \frac {V}{R}\]

Now, placing the value of equation (2) in equation (1) we get:

\[ P = \frac {V^{2}}{R} \]

From the above derivations, we got the following conclusion:

Power and Resistance in Electronics

In electronics, we define power as the rate of doing work. So, what kind of work is being done in electronics? Is it the normal work that we do daily or something else?  Let’s describe it with a simple statement:

We define resistance as the opposition offered against the flow of electrons in the circuit. It means that the more is the obstruction, the more is the work done per unit time to make them flow, i.e. the more is the power required to make their flow easy.

From the above statement, we cannot deny the fact that the relation between power and resistance is proportional. 

Moreover, both power and resistance are important factors to consider for making electrical appliances that should not be neglected in any case.