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Power - Definition, Unit, Efficiency, Examples

Let’s consider two men A and B. A is able to do 10 J of work in 1 hour, but B is able to do only 5 J of work in the same amount of time. Who is more powerful? We say that person A is more powerful because he is able to do a higher amount of work in the same time, compared to B. Let us take two electrical bulbs B1 and B2. If you look closely at both bulbs, they have a unique “power rating”. If bulb B1 is rated at 25 watt and B2 at 50 watt, we say that B2 consumes more power.

You may also want to learn what is Ohm's law.

What is Power?

Power is defined as the amount of work done or energy converted in a given amount of time. Mathematically, it can be expressed as 

image

where W is the work done in Joule and t is the time taken in seconds. From the above equation, it is clear that more power is consumed or delivered when a large amount of work is done in a short period of time.

The SI unit of power is J/s or watt. Its symbol is W.

You may also want to learn about capacitors and capacitors uses.  

What is Instantaneous Power?

Instantaneous power is defined as the amount of work dW in a time interval dt. Mathematically, we can say that 

P = image ; where dW is the amount of work done in time dt. Since dW=F.dx; where F is the force applied and dx is the displacement.image 

Since power is a vector dot product , it is a scalar quantity.

What is Average Power?

Average power is defined as the total work done W in a total amount of time interval t

image

What is Efficiency?

Efficiency(n) is the outpower power delivered divided by the input power supplied. Mathematically, it can also be expressed in percentage 

image

Note: Efficiency of a machine is always less than 100 %

Power in Case When Force is Applied but There is No Displacement:

For such a case, velocity v=0. Therefore power delivered = zero.

Power When Body is in Uniform Motion

For a given magnitude of force:

  1. When the direction of force does not change, power is constant, since

 imageis constant in this case.

  1. When the direction of force changes, power is variable, since

 imageis variable in this case.

Practice Problems of Power

Question.1 A body of mass 1 kg begins to move under the action of a time dependent force, F = (2t i + 3t2 j ) N, where i and j are unit vectors along the x and y axes. What power will be developed by the force at a time t

  1.  

image

 

2) An engine pumps 400 kg of water through a height of 10 m in 40 s. Find the power of the engine if its efficiency is 80%(Take g =10 ms-2 ).

Question.2 1 kW (b) 2 kW (c) 2.5 kW (d) 1.25 kW

Solution (d)

Work done in raising the water against gravity W = mgh ; 

W = 400 × 10 × 10 = 40 kJ

Power used by the engine = image

The efficiency of the engine is n=  image

 now to find power input we will use,

 image

Input power = 1 kW0.8 = 1.25 kW.

Question.3 Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine ? (g =10 ms-2)

  1. 12.3 kW (b) 7 kW (c) 8.1 kW (d) 10.2 kW

Solution) c

Power available in falling water = 15 × 10 × 60 = 9000 W; since 10% of energy is lost

Remaining Energy = 90 % of 9000 = 8100= 8.1 kW.

Question.4 If image ms-1, then find the instantaneous power

(a)195 W (b)45 W (c)75 W (d) 100 W

Solution) b

image

FAQs of Power

Question.1 What is the unit of power?

Answer) The unit of power is J/s or watt.

Question.2 Is Power a scalar or vector quantity?

Answer) Power is a Scalar quantity.

Question.3 When the angle between the force(F) and velocity (v) is 900 ; then the power delivered is 

Answer) Since P= F .v = Fvcos ; =900  

∴ P= zero. 

Question.4 What is efficiency?

Answer) It is the ratio of the output power delivered to the input power supplied

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