Circuit Theory

Basics

POWER AND ENERGY

Power:

Power is nothing but

  • the rate at which the work is done $$p (t)=\frac{dW}{dt}$$
  • the rate of expending or consuming energy. $$p (t)=\frac{dE}{dt}$$

Unit:

  • watt $(W)$
  • joules/second $(J/s)$ (since Work-done per unit time)
  • Also, Work done = Force × distance, hence unit of power can be $Nm/s$

Note: In electrical terms, we are using watts only

Practice Question

🌾In mks unit, watt is

a) $J/s$

b) $Js$ 

c) $J/s^2$ 

d) none of these

Correct Answer: Option A

In terms of V and I:

As we know, $$p (t)=\frac {dW}{dt} $$Rewritting this as $$p(t)=\frac {dW}{dq}×\frac{dq}{dt}$$Since $v (t)=dW/dq $ and $i (t)=dq/dt $$$p (t)=v (t)\;i (t) $$

Horsepower:

This term was used by James Watt for marketing his improvised steam engine, as it was the easy way to explain people at that time.

“This engine can do the work of $10$ horses = $10$ HP engine”$$1HP=746 \;watts$$

Nowadays we are using this term to measure the output power of engines, motors, etc.