Notes : Power , Defination, Unit and Dimensions - Class 11 Physics

Notes : Power , Defination, Unit and Dimensions - Class 11 Physics chapter 5 work energy and power

1. Definition of Power

Power is the rate at which work is done or energy is transferred.

$$ P=\frac{W}{t} $$

Where:

• \(P\) = Power
• \(W\) = Work done
• \(t\) = Time taken

2. Nature of Power

• Power is a scalar quantity.
• It has only magnitude, no direction.
• It can be positive, negative, or zero depending on work done.

3. Dimensional Formula of Power

$$ [W]=[ML^2T^{-2}] $$ $$ P=\frac{W}{t} $$ $$ [P]=[ML^2T^{-3}] $$

4. Units of Power

SI Unit

$$ 1\,W = 1\,J\,s^{-1} $$

Horse Power

$$ 1\,hp = 746\,W $$

Kilowatt

$$ 1\,kW = 1000\,W $$

Kilowatt-hour (Energy Unit)

$$ 1\,kWh = 3.6 \times 10^6\,J $$

Note: kWh is a unit of energy, not power.

5. Types of Power

Average Power

$$ P_{avg}=\frac{W}{t} $$

Instantaneous Power

$$ P=\vec{F}\cdot\vec{v} $$ $$ P=Fv\cos\theta $$

• \(\theta = 0^\circ \Rightarrow P = Fv\) (maximum)
• \(\theta = 90^\circ \Rightarrow P = 0\)
• \(\theta = 180^\circ \Rightarrow P = -Fv\)

6. Important Relations

$$ P = Fv $$ $$ P = \frac{dW}{dt} $$

7. Solved Example: Elevator Problem

Example 5.10An elevator can carry a maximum load of 1800 kg (elevator + passengers) and is moving up with a constant speed of 2 m s⁻¹.The frictional force opposing the motion is 4000 N. Determine the minimum power delivered by the motor to the elevator in watts as well as in horsepower

Given Data

• \(m = 1800\,kg\)
• \(v = 2\,m\,s^{-1}\)
• \(F_f = 4000\,N\)
• \(g = 10\,m\,s^{-2}\)

Step 1: Weight of Elevator

$$ W = mg $$ 

 $$ W = 1800 \times 10 = 18000\,N $$

Step 2: Total Opposing Force

$$ F_{total} = W + F_f $$ 

 $$ F_{total} = 18000 + 4000 = 22000\,N $$

Step 3: Power

$$ P = Fv $$ 

 $$ P = 22000 \times 2 = 44000\,W $$

Step 4: Convert to Horse Power

$$ P = \frac{44000}{746} $$

 $$ P \approx 59\,hp $$

Final Answer

$$ P = 44000\,W \approx 59\,hp $$

8. Key Points

• Power measures rate of doing work.
• SI unit is Watt (W).
• \(1\,hp = 746\,W\).
• \(kWh\) is energy, not power.
• Power is scalar.

9. FAQ

What is power?

Power is the rate of doing work.

What is its SI unit?

Watt (W)

Is power a vector?

No, it is a scalar quantity.

10. MCQs

1. Power is:
   (a) Force × time
   (b) Work × time
   (c) Work/time
   (d) Energy × time
   Ans: (c)
2. SI unit of power:
   (a) Joule
   (b) Watt
   (c) Newton
   (d) Pascal
   Ans: (b)
3. 1 hp equals:
   (a) 1000 W
   (b) 746 W
   (c) 500 W
   (d) 100 W
   Ans: (b)