# Power

• Last Updated : 15 Sep, 2022

Power in Physics is defined as the time rate of the amount of energy converted or transferred. In the SI system (or International System of Units), Watt (W) is the unit of Power. Watt is equal to one joule per second. In earlier studies, power is sometimes called Activity. Power is a scalar quantity. Power is always a function of Work done, therefore if a person works at a variable rate depending on the time of day, his power will likewise vary. The idea of Average power enters the picture at this point. Let’s study Power, average power, unit, and formula in this Article. ## What is Power?

Power is a physical quantity that is a measure of energy transfer rate. Therefore, it can be defined as the rate at which work is done with respect to time.

Hence, Power is the amount of energy consumed per second. Power can also be defined as the quantity of force required to cause a unit displacement. Power is a scalar quantity and is denoted by P.

For example, a bulb with a higher power or wattage, like 100 W, illuminate more light than a light bulb of 10 W. Thus, this implies that more energy is illuminated by the bulb consuming more power.

## Power Formulas

Power is defined as the time rate of work done by the object, then, mathematically this can be given by the power formula as:

P = W ⁄ t

where,

W is the Work done,

t is the Time for which work is done, and

P is the Power gain or loss.

Hence, the above relation of Power is called work-time equation

Work done (W) by an object can be defined as the product of force and the displacement of the object, then the power formula in terms of force is given by-

Since, W = F × s

where,

F is the force required, and

s is displacement of the object.

Therefore,

P = F × s ⁄ t

Since, the velocity of the object, v = s / t

Then,

P = F × v

Hence, the above relation is known as force-velocity equation

## Units of Power

• The SI unit of Power is Watt (W) whose multiples are: KW, MW, GW…

A Watt is defined as, when a body does work of one joule in one second it is called One-Watt Power.

1 Watt (W) = 1 Joule (J) / 1 Second (s)

• Another unit of power is Horsepower (hp), where 1 hp = 746 W
• Dimensional Formula for Power is [ML2T3]

## Average Power

Average Power is defined as the ratio of the net (Total) work done in the total amount of time. Thus average power is given as,

Average Power = Total Work Done / Total Time Taken

or

Pav = ΔW / ΔT

where,

Pav is the Average Power,

ΔW is the Total Work Done, and

ΔT is the total amount of time taken.

In case when the rate of work done by the body is uniform or constant then the average and instantaneous power become equal.

## Mechanical Power

In mechanical systems, the sum of forces and motion is known as power. Power is generally the product of a force acting on an object multiplied by its velocity, or the result of torque acting on a shaft multiplied by its angular velocity.

The time derivative of work is another way to define mechanical power. Hence, the mechanical power is given by.

Mechanical Power = Force × velocity

or

Pm = F × v

## Electrical Power

The rate at which energy is changed from the electrical energy of moving charges to another form, expressed as a rate, per unit of time, is known as electric power.

Mathematically, electric power is defined as the product voltage and the current flowing, given as:

P = V × I

According to Ohm’s Law. V = I × R, therefore:

P = I2 × R

or

P = V2 / R

where,

P is the electric power,

I is the current flowing,

R is the resistance and

V is the voltage.

## Calculating Power and Energy Consumption

The power and energy consumption are measured by a formula. According to this, multiplying the number of power units consumed within the period over which it has been consumed gives it energy consumption.

Hence, the energy consumption formula or the power consumption formula can be stated as:

E = P × (t/1000)

where,

• E is the Energy consumed or power consumed
• P is the power and
• t is the time over which the power or energy was consumed.

The Energy consumed or power consumed is generally measured in Joules or kilowatt-hours (kWh),

## Solved Examples on Power

Example 1: A boy pushes a box of 20 kg up to a distance of 5 m for 10 seconds. Calculate the power delivered to the box.

Solution:

Given,

Mass of the box, m = 20 kg

Displacement covered, d = 5 m

Time of displacement, t = 10 s

Weight of the box, F = mg = 20 ×10 N = 200 N

Work done by the boy, W = F d = 200 N ×5 J = 1000 J

Power delivered, P = W ⁄ t = 1000 / (10 J/s) = 100 J/s

Hence, power delivered to the box is 100 J/s.

Example 2: A pump is required to lift 500 kg of water per minute from an 8 m deep well and eject it with a speed of 25 m/s. Calculate the power of the pump.

Solution:

Given,

Mass of the water, m = 500 kg

Height covered, h = 8 m

Eject velocity of water, v = 25 m/s

Delivery time, t = 1 min = 60 s

Total energy is converted into work, W = E = m g h+(1/2) m v2

= (500×10×8)+(500×25×25)/2

= (40000+156250) J

=196250 J

Power delivered, P = W / t

=196250 J / 60 J

= 3271 W

Hence, power delivered by pump is 3271 W.

Example 3: An elevator is designed to lift a load of 500 kg through 5 floors of a building averaging 3 m per floor in 5 seconds. Calculate the power of the elevator.

Solution:

Given:

Mass of the load, m = 500 kg

Total height covered, h = 5 × 3 m =15 m

Time taken, t = 5 s

Power delivered by elevator, P = W ⁄ t = mgh ⁄ t

= (500 × 10 × 15) / 5 W

=15000 W

=1.5×104 W

Hence, power of the elevator is 1.5×104 W.

Example 4: A force of 5 N is required to move a body on a frictional floor with a constant velocity of 5 m/s. Find the power generated by the force.

Solution:

Given:

Velocity of body, v = 5 m/s

Force required to maintain the velocity, F = 5 N

Power generated, P = 5 × 5 W

= 25 W

Hence, power generated by the force is 25 W.

## FAQs on Power

Question 1: Can the concept of power help us describe how objects move?

Work done and time are connected in the power equation. Since forces may move objects and we know that forces perform work, we might assume that by understanding the power, we can gain insight into how a body moves through time.

Question 2: What is Power in Physics?

Power is the amount of energy consumed per second. Power can also be defined as the quantity of force required to cause a unit displacement.

Question 3: How to find Power?

Power can be determined by the formula:

P = W ⁄ t

where

• W is the Work done,
• t is the Time for which work is done, and
• P is the Power gain or loss.

Question 4: What is the difference between Power and Energy?

Energy is defined as the ability to do some physical work, e.g playing, jumping, etc. However, power is defined as the rate at which the energy is transferred, or the work is completed.

Question 5: What happens to a body on which work is done?