What is Power Formula – Definition, SI Unit, Examples with Related Equation

Definition of Power

The amount of energy converted or transferred per unit of time or the rate of doing work per unit of time is called Power. 

Power Formula:   P = Work done by an object (W)/ Total Time Taken (t) 

P = W/t or P = E/t

Where work done is measured in Joule (J) and Time is measured in Seconds or Minutes 

In simple words, power is measured by the total work done by an object divided by the total time taken or required by an object to complete that work.

SI Unit Of Power

The SI unit of power is Watt (W) which is used in honor of Scottish inventor James Watt.

One watt equals one joule per second (1W = 1J / 1s)

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Power Formula can be written in different forms as per the required statement

1. P = V X I

When there is a numerical or problem statement to find out the power (P) of the electrical circuits, we use this formula using Potential Difference (V) and Current (I). This formula is also called Ohm’s Law.

2. P = I^2 X R or P = V^2 / R

The above-mentioned formulas are just modified versions of Ohm’s Law using the basic electrical formula V = I X R where V is the potential difference, I is the current and R is the resistance of the electrical circuit.

3. P = F X D / T

The above formula is used when work done is given using the force applied (F) on the object where D is the displacement of the object and T is the time taken by the object.

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Some examples using the above formulas

Q1. A person applies a force of 50N on an object and moves 15 meters far from its initial position in 20 seconds. Find the power done by the object.

Solution – We have the formula to find out power using force i.e. P = F X D /T

                                      Here. F = 50 N

                                               D = 15 m

                                               T = 20 seconds

                                               P =?

By putting the values, we have

                                               P = 50 X 15 / 20

                                                P = 37.5 W

Hence, 37.5 W is the answer

Q2. Is an electrical circuit having a resistance of 50 Ohm connected with a potential difference of 10 V. Find out the power of the electrical circuit?

Solution –  We have the formula to solve this numerical i.e. P = V^2/R

                                         Here, P =?

                                                   V = 10 v

                                                   R = 50 ohm

Putting the values in the above equation, we have

                                         P = 10^2/50

                                          = 100/50

                                           P = 2 W

Hence, 2 W is the answer

Important Question From Power Chapter

Question.1 Does work done depend upon the velocity of the body?
Answer. No.

Question.2 State the law of conservation of energy.
Answer. It states that energy can neither be created nor destroyed.

Question.3 In a tug-of-war one team gives way to the other. What work is being done and by whom?
Answer. The winning team does work. The work is equal to the product of the resultant force and the displacement undergone by the losing team.

Question.4 What will cause a greater change in the kinetic energy of a body? Changing its mass or changing its velocity?
Answer. Changing its velocity.

Question.5 List two essential conditions for work to be done.
Answer. (i) A force must act and (ii) There should be displacement in the body.

Question.6 When is 1 joule of work said to be done?
Answer. When a force of 1 newton acting on a body displaces it in its own direction.

Question.7 What is the SI unit of work done and power?
Answer. Joule and Watt.

Question.8 What is power? What is its SI unit?
Answer. It is defined as the rate of doing work. Its unit is the watt.

Question.9 Find the energy in kWh consumed in 10 hours by a machine of power 500 W.
Answer. W = P x t = 500 x 10 = 5000 Wh – 5 kWh.

Question.10. When is work said to be done against the force of gravity?
Answer. When a body is lifted the work is done against the force of gravity.

Question.11 Write an expression for the work done in lifting a body of mass ‘m’ through a vertical height ‘h’.
Answer. Work done W = mg, where g is the acceleration due to gravity.

Question.12 When a book is lifted from a table, against which force work is done?
Answer. Work is done against the force of gravity.

Question.13 Will work be done by a man who pushes a wall?
Answer. No.

Question.14 What is the work done when the force acting on the body and the displacement produced in the body are at right angles to each other?
Answer. Zero.

Question.15 Is it possible that some force is acting on a body but still the work done is zero?
Answer. Yes, when a force acts at an angle of 90° with the displacement.

Question.16 What is the work done on a body moving in a circular path?
Answer. Zero, because force and displacement are perpendicular to each other.

Question.17 A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force. Let us take it that the force acts on the object through displacement. What is the work done in this case?
Answer. Given, displacement = 8 m, 
Force = 7N
Now, Work done = Force x Displacement
= 7 x 8 
= 56 J

Question.18 When do we say that work is done? 
Answer. Work is said to be done when a force causes displacement of an object in the direction of the applied force.

Question.19 Write an expression for the work done when a force is acting on an object in the direction of its displacement.
Answer. Work done = Force x Displacement

Question.20 A pair of bullocks exerts a force of 140 N on a plow. The field being plowed is 15 m long. How much work is done in plowing the length of the field?
Answer. Work done = Force x Displacement = 140 x 15 = 2100 J.