- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Electric Power and Efficiency of Electric Device

## Power or Electric Power

The rate at which work is done in an electric circuit is called as *electric power*. In other word, the work done per unit time is termed as *electric power*. It is denoted *p* or P.

## Formula and Unit of Power

When voltage is applied across a resistor, it causes current to flow through it. Therefore, work is being done in moving the electrons through the resistor in a unit time is called the electric power.

Referring the above figure,

$$\mathrm{V=\frac{work}{Q}}$$

$$\mathrm{\Rightarrow work(W)=VQ=VIt}$$

As, the power is defined as work done per unit time i.e.

$$\mathrm{Power(P)=\frac{work\:done\:in\:electric\:circuit(W)}{Time(t)}=\frac{VIt}{t}}$$

$$\mathrm{(∵V=IR\:or\:I=\frac{V}{R})}$$

$$\mathrm{∴P=VI=I^2R=\frac{V^2}{R}}$$

The above three formulae are equally valid for power calculation. Which one is used depends on the known quantities.

Since, the work done is measure in *joules* and time in *seconds*. Therefore, the unit of power is *joule/sec* or ** watt** i.e.

$$\mathrm{Unit\:of\:Power=\frac{joule}{seconds}=watt}$$

Hence, the power consumed in an electric circuit is 1 watt, if a potential difference of 1 V causes 1 A current to flow through the circuit.

The larger units of power are *Kilowatts (kW) Megawatts (MW)*, and *Gigawatts (GW)*.

$$\mathrm{1\:kW=1000\:W;1MW=10^6\:W=10^3\:kW;1\:GW=10^9W}$$

Sometimes, power is also measured in *Horse Power* (h.p.),

1 horse power (h.p.) = 746 Watts

## Expressions of the power

Expressions of power in the

*translational system*,

$$\mathrm{Power=\frac{Work\:Done}{Time}=\frac{Force×Distance}{Time}=Force×Velocity}$$

Expression of power in the

*rotational system,*If a body makes N r.p.m. and the torque acting on it is τ Newton-meter, then,

$$\mathrm{Work\:done/minute = 2\pi Nτ\:joules}$$

$$\mathrm{Work\:done/sec =\frac{2\pi Nτ}{60}joules/sec}$$

Therefore,

$$\mathrm{Power(P)=\frac{2\pi Nτ}{60}joules/sec\:or\:watts}$$

$$\mathrm{(∵\:746\:watts = 1 h. p. )}$$

$$\mathrm{∴\:Power\:(P)=\frac{2\pi Nτ}{60×746}h.p}$$

## Efficiency of Electric Device

The efficiency of an electric device is defined as the ratio of useful output power to the input power, i.e.,

$$\mathrm{Efficiency(\eta)=\frac{Useful\:Output\:Power(P_{o})}{Input\:Power(P_{i})}}$$

As, the efficiency is the ratio of output and input powers, thus it is a dimensionless quantity. Generally, the efficiency of a device is measured in percentage (%), as,

$$\mathrm{\%\:Efficiency(\eta)=\frac{Useful\:Output\:Power(P_{o})}{Input\:Power(P_{i})} × 100 \%}$$

Some electrical devices have efficiency nearly equal to 100%. An example of such device is *electric heater*, in which all the input electrical energy is converted into heat energy.

## Harmful Effects of Poor Efficiency

The harmful effects of poor efficiency are as follows −

Poor efficiency of the device means greater the losses, thus a large amount of energy is wasted on non-useful output.

The non-useful output appears in the form of heat that raises the temperature of the device. Therefore, poor efficiency means a significant temperature rise. The devices that run hot are more likely to fail.

The heat produced due to poor efficiency has to be dissipated. Thus, the heat removal system increases the cost and size of the device.

## Numerical Example - 1

An electric motor is developing a torque of 60 N-m at a speed of 1500 r.p.m. Calculate the power developed by the motor in Watt and h.p.

**Solution**

$$\mathrm{Power\:developed\:by\:motor,P=\frac{2\pi Nτ}{60}=\frac{2\pi×1500×60}{60}=9420 W}$$

$$\mathrm{(∵\:746\:Watts = 1 h. p. )}$$

$$\mathrm{∴p=\frac{Power\:in\:watts}{746}=\frac{9420}{746}=12.63 h. p.}$$

## Numerical Example - 2

A lift of 200 kg mass is raised with a velocity of 10 m/s. if the input power to the driving motor is 21.42 kW. Calculate the % efficiency of the motor.

**Solution**

Weight of the lift,*F = mg* = 200 × 9.81 = 1962 Newton

Output power of the motor = Force × Velocity = 1962 × 10 = 19620 W = 19.62 kW

$$\mathrm{\%\:Efficiency=\frac{Output\:power\:of\:motor}{Input\:power\:of\:motor}× 100\:\%\:=\frac{19.62}{21.42}× 100 = 91.59\%}$$

## Numerical Example -3

A resistor of 100 Ω has a voltage of 120 V across it. Calculate the power absorbed by the resistor.

**Solution**

Power abosrbed by resistor,

$$\mathrm{p=\frac{V^2}{R}=\frac{(120)^2}{100}=144 W}$$

- Related Articles
- Electric Machine Losses and Efficiency with Examples
- Three-Phase Electric Power
- What is Electric Power?
- Electric Power System and Equipment – Voltage Ratings
- Electric Power Distribution System Basics
- Electric Traction: Power Output and Energy Output at Driving Axles
- Overview of Electric Current, Voltage, and Resistance Electric Current
- Difference between Electric Current and Electric Charge
- Relation between Electric Field and Electric Potential
- Electric Breaking of DC Motors – Types of Electric Breaking
- (a) Name one device which works on the magnetic effect of current.(b) Name one device which works on the phenomenon of electromagnetic induction. (c) Which device converts electric energy into mechanical energy? (d) Describe the principle of working of an electric motor. (e) Explain the principle of working of an electric generator.
- On which principal does electric motor and electric generator work ?
- Name the device used these days in place of electric fuses in electrical circuits.
- Types of Electric Motors Used in Industrial Electric Drives
- Fill in the blanks :$(a)$. A device that is used to break an electric circuit is called _______________.$(b)$. An electric cell has _______________