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Power is defined as the time rate of doing work. The SI unit of power is Watt (W) which is joules per second (J/s). It is a scalar quantity.
Also Read: Difference Between Scalar and Vector Quantities
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Key Terms: Force, Energy, Work, Time, Si Unit, Scalar Quantity, Vector Quantity
What is power?
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Power is defined as the rate of doing work in the minimum possible time.
- It is the amount of work or energy that is transferred per unit of time.
- Power is directly proportional to energy and work done. The more work done or energy consumed, the more will be power.
- Power is directly proportional to work and is inversely proportional to time.
- Power is also used to calculate the efficiency of the device. The formula is
Efficiency= output power/ input power
- The SI unit of power is Watt.
- Formula of Power:
Where;
E = Energy
T = Time
| P= E/ T |
power
Formula Of Power In Terms Of Force
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The formula of power in terms of force is
| P=W/T |
As we know;
Work= force × displacement (f.s)
P=W/T = f.s/t
Also Read:
| Topic Related Power | ||
|---|---|---|
| Electric Power Formula | Unit of Power | Power Of Alternating Current |
Average Power
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The average power is defined as the total amount of work done or energy used per total time. It is the ratio of total work done and total time taken.
The formula of average power
| Pav = ΔW/ ΔT |
There are a number of instruments that are used to calculate the average power. One such instrument is the fibre optic power instrument. It is used to compute the average power of a continuous light beam which is used to test the power of a signal in a fibre optic network.
Average power
Electrical Energy
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Electrical energy is defined as the rate at which the electrical energy of the moving charges is transformed into some other form of energy like mechanical energy, heat energy, etc.
Electric generators transform mechanical energy obtained from an outside source into electrical energy.
The electrical power formula
| P= VI |
Where;
P = Power
V = Potential Difference
I = Electric Current
According to Ohm's Law V= IR,
So;
P= I2R
Where; R = resistance in the circuit.
Through this formula, what we derive is that
Power is directly proportional to the current and also the heat generated due to resistance in the circuit which means that the more the electric current in the circuit, the more will the power and so will the heat generated or the amount of energy transferred per unit time.
Also Read:
| Chapter Related Topic | ||
|---|---|---|
| Difference between Watts and Volts | Relation Between Watts and Volts | Work and Energy |
Important PYQs Based On Power
- An Installation Consisting Of An Electric Motor… [VITEEE 2014]
- Which Of The Following Must Be Known In Order To…. [BITSAT 2012]
- A Motor Of Power P 0 Is Used To Deliver Water At A…. [VITEEE 2009]
- A Coil Of Inductive Reactance 31 Has A Resistance…. [NEET 2006]
- A 30 V 90 W Lamp Is Operated On A 120 V Dc Line A… [VITEEE 2015]
- A Constant Power Is Supplied To A Rotating Disc Th…. [CBSE Class XII]
- An Electric Bulb Is Rated 220 V And 100 W What Is…. [JKCET 2019]
- A Force Of 2 I 3 J 4 K N Acts On A Body For 4 Seco…. [BITSAT 2019]
- A 100 W 200v Bulb Is Connected To A To V Power Sup…. [JIPMER 2000]
- A Particle Of Mass M Starting From Rest Undergoes… [NEET 2010]
- A Ball Moving With Velocity 2 M S Collides Head On…. [NEET 2010]
- Two Masses Of 1 G And 9 G Are Moving With Equal Ki… [NEET 1993]
- A Batsman Hits Back A Ball Straight In The Directi… [NEET 1989]
- A Bullet Of Mass 10 G Leaves A Rifle At An Initial… [NEET 1989]
- On A Frictionless Surface A Block Of Mass M Moving… [NEET 2015]
- Two Particles Of Masses M 1 M 2 Move With Initial…. [NEET 2015]
- A Particle Moves From A Point 2 I 5 J To 4 J 3 K W…. [NEET 2016]
- The Potential Energy Of A Particle In A Force Fiel…. [NEET 2012]
- Two Spheres A And B Of Masses M 1 And M 2 Respecti…. [NEET 2012]
- Find The Torque About The Origin When A Force Of 3… [NEET 2020]
Things To Remember
- Power is a scalar quantity
- Power is defined as the time rate of doing work.
- The SI unit of power is Watt.
- Power is also used to calculate the efficiency of the device.
- There are a number of instruments that are used to calculate the average power.
Sample Question
Ques. A man weighing 60 kilograms climbs up a staircase with a bag of 20KG on his head. The staircase has 20 steps each of 0.2 meters in height. What will be the power utilized if he climbs the staircase in 10 seconds? (2 Marks)
Ans. Height of staircase = 20×0.2 = 40m
P= W/T = E/T = mgh/T
M = 60+20 = 80 kilograms
= 80×9.8×4 /10
= 78.4 × 4
Power = 31.36 Watt.
Ques. Define power, and obtain an expression for instantaneous power by mentioning the units of power. (3 Marks)
Ans. Power is defined as the time rate at which work is done or energy is transferred.
The instantaneous power is defined as the limiting value of the average power as the time interval approaches zero.
P=dw/dt
P= d F.s/dt (where f and s are to be taken as scalar quantities)
= F.ds/ dt = V (as V= s/t)
P= F×V
P= Fv cos theta
Units of power:- The SI unit of Power is Watt.
It can also be calculated in kilowatt (kw), megawatt (mw) and horsepower (hp)
1 Kw = 10³ watt
1 Mw = 106
1 hp = 746 watt
The dimensional formula of power is= ML-2T-3
Ques. If Riya has a weight of 60 kg and she runs up to a height of 13m in 50 sec, what is the power consumed? Take g= 10ms2. (2 Marks)
Ans. Given mass = 60kg
Height = 13m, time= 50sec, g= 10ms²
We know that,
P= W/T = mgh/T
I.e., 60×10×13/50
So, P= 156 Watt
Ques. 15. A pump on the ground floor of a building can pump up water to fill a tank of a volume of 30 m3 in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump? (3 Marks)
Ans. Here,
volume of water = 30 m3 , t = 15 min = 15 x 60 = 900s
h = 40 m, efficiency= 30%
As the density of water = p = 103 kg m-3
Mass of water pumped, m = volume x density = 30 x 103 kg
Actual power consumed or output power p0 = W/t = mgh/t
=>p0=(30 x 103 x 9.8 x 40)/900=13070 watt
If pi is input power (required), then as
efficiency = p0/pi=> pi=p0/η = 13070/(30/100)=43567 W =43.56 KW.
Ques. Define average power. (1 Mark)
Ans. The average power is defined as the total amount of work done or energy used per total time. It is the ratio of total work done and total time taken.
The formula of average power: Pav = ΔW/ ΔT
Ques. What is electrical power? (2 Marks)
Ans. Electrical energy is defined as the rate at which the electrical energy of the moving charges is transformed into some other form of energy like mechanical energy, heat energy, etc.
Electric Generators transform mechanical energy that is obtained from an outside source into electrical energy.
The electrical power formula: P= VI
Ques. What is the formula for electrical power and average power? (1 Mark)
Ans. Formula for electrical power is = P= VI
And formula for average power is = Pav = ΔW/ ΔT
Ques. Differentiate power and energy. (3 Marks)
Ans. differenced are:
| Energy | Power |
|---|---|
| Capacity to do work | Rate at which work is done |
| Energy is power integrated over time | Energy is transmitted |
| Symbol - W | Symbol - P |
| Unit - Joule = Watt-Sec | Unit - Watt = Joules/Sec |
Ques. Which of the formula is used to find power? (1 Mark)
(a) Power = 2(Force – Velocity)
(b) Power = Force * Velocity
(c) Power = Force / Velocity
(d) Power = Force + Velocity
Ans. b. Power = Force * Velocity
Explanation: Power = Work/Time
Power = (Force*Displacement)/Time
Power = Force (Displacement/Time)
Power = Force * Velocity
Ques. A watt is equivalent to (1 Mark)
(a) Newton
(b) Joules
(c) Joule/second
(d) Newton/second
Ans. c. Joule/Second
Explanation: Watt = Joule/second = 1 newton meter per second
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