Power

 

Power

 Work is manifestation of energy.

Work done = Energy Consumed.

Application of Force (Pressure) to any object results in its movement (Displacement)

Work done is applied Force multiply by Distance moved by object in the direction of force.

 Work = Force × Distance (in direction of force)

 Dividing by Time, we get        Work                         Distance

-----------  =  Force ×  -----------

   Time                         Time

 Work divided by time is Power.

 Distance divided by time is Velocity (in direction of force)

 Therefore     Power = Force × Velocity   OR   P = F × V

 Three conditions based on direction of force,

 When force is in the direction of object can move.

 Power P = F × V

When force is in the direction perpendicular to object can move.

   

Power P = F × 0 = 0  (No movement in direction of force)

Force adds only friction results in energy loss

When force is in the direction oblique to object can move.

 Force at angle θ to direction of movement as shown

 Force F can have two components.

F_x = FCosθ in the direction of displacement and

F_y = FSinθ perpendicular to direction of displacement

 Power by component F_x

P_x = F_x × D  =  FCosθ  × D =  FDCosθ

 Power by component F_y

P_y = F_y × 0  (No movement in direction of force F_y)

Force F_y adds only friction results in energy loss

Similarly in the Electrical System

Application of Electro Motive Force (EMF) in the circuit results in movement of Electrons.

EMF is Voltage represented by V

Rate of flow of electrons is Current represented by I

 Electrical Power = Electrical Force V × Rate of electron displacement I along the force V

 Three conditions based on direction of V and I

       A. Direction of the current I is same as voltage V as in purely resistive circuits

Power = Voltage × Current

P = V × I

2. Direction of the current I is perpendicular to voltage V as in purely inductive or capacitive circuits

Power = 0 as no current along the voltage. Only cause Losses. 

3. When direction of the current I is oblique to the voltage V as in mixed RL or RC or RLC circuits. 

 Force V at angle θ WRT current as shown

 Force V can have two components.

V_x = VCosθ in the direction of Current and

V_y = VSinθ perpendicular to direction of Current

 

Power by Component V_x

P_x = VCosθ × I = VICosθ

 

Power by Component V_y

Power P_y = VSinθ × I = VISinθ

 

P_x is power useful for the work known as Active Power

P_y is power useless for the work known as Reactive Power that only adds losses.