Relation Between Power and Resistance

Relation Between Power and Resistance in Detail

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. \[P = \frac{V^{2}}{R}\]. 


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.

  1. 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 Power?

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: 30/2 = 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


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

I is measured in Ampere.

What is Resistance?

While driving a car with 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.

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:

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


I = 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 the 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 easy flow.

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

FAQs (Frequently Asked Questions)

Question 1: What is the Difference Between the Current and the Voltage?

Answer: We define current as of the EMF of the source divided by the total resistance in the circuit. Voltage is the power offered to push the current through the circuit.

Question 2: What is the Power in Physics?

Answer: In physics, power is the amount of energy transmitted or converted in a unit of. In the International System of Units or SI, the unit of power is the watt, which is equal to one Joule per second. In other words, power is called activity. Power is a scalar quantity.

Question 3: Are Power and Resistance a Vector or a Scalar Quantity?

Answer: Resistance and power are scalar quantities. These two quantities have magnitude but no direction.

Question 4: State Real-Life Applications of Resistance.

Answer: We find the application of resistance in the following five places:

  • Mobile phone chargers.

  • Potentiometer - electric fan speed controller.

  • Metallic film of the lightning bulb.

  • Street lights (LDR).

  • Chargers of a laptop.

Question 5: State the Use of Ohm’s Law in Daily Lives.

Answer: We fine six uses of Ohm’s law in our day-to-day lives:

  • Domestic fans

  • Electric heaters

  • Electric kettles and iron

  • Electric devices designing

  • Fuse designing

  • Mobile/laptop charger

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