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Power - Meaning, Unit, Formula, FAQs

Power - Meaning, Unit, Formula, FAQs

Edited By Vishal kumar | Updated on Aug 30, 2024 03:36 PM IST

Power in physics refers to the amount of work done or energy transferred per unit of time. It is expressed in watts (W) and a watt is the equivalent of one joule per second. Power measures, how fast the energy is used or converted to another form. In electrical systems, for e.g. power = voltage x current (in a charge-neutral case, what this really tells you is how much electrical energy is being consumed, or being pumped, per unit of time. Power is important in running the various types of equipment and machines we use in everyday life. Generally, the higher the power rating, the more work a device can do in less time.

This Story also Contains
  1. What Is Power
  2. Solved Example Based on Power
  3. Conclusion

In this article, we are going to read about power and different types of power and also see some solved examples, which belong to the chapter work, energy, and Power, which is one of the important chapters in Class 11 physics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE and more. Over the last ten years of the JEE Main exam (from 2013 to 2023), more than fifteen questions have been asked on this concept. And for NEET almost six questions were asked from this concept.

Let's read this entire article to gain an in-depth understanding of the concept of power.

What Is Power

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

Dimension- $M L^2 T^{-3}$

Units - Watt or Joule/sec (in SI), Erg/sec (in CGS)

Average power

$P_{a v}=\frac{\Delta w}{\Delta t}=\frac{\int_0^t p \cdot d t}{\int_0^t d t}$

Instantaneous power

$P=\frac{d w}{d t}=P=\vec{F} \cdot \vec{v}$

Where, $\vec{F} \rightarrow$ force $\vec{v} \rightarrow$ velocity

Power is expressed as the rate of change of kinetic Energy

$P=\frac{d k}{d t}$

Where,

$\begin{aligned} & d k \rightarrow \text { change in kinetic energy } \\ & \qquad d t \rightarrow \text { interval of time }\end{aligned}$

i.e. power is equal to the scalar product of force with velocity

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Solved Example Based on Power

Example 1: An engine of a car of mass m = 1000 Kg changes its velocity from 5 m/s to 25 m/s in 5 minutes. The power (in KW) of the engine is

1) 5

2) 2

3) 1

4) 4

Solution:

Power expressed as the rate of change of kinetic Energy -

Power = Work done / time = change in K.E / time

Power = dk/dt

$\begin{aligned} & P=\frac{\frac{1}{2} m\left[(25)^2-(5)^2\right]}{5 \times 60} \\ & =\frac{\frac{1}{2} \times 1000 \times 600}{5 \times 60}=1000 \mathrm{~W} \\ & P=1 \mathrm{KW}\end{aligned}$

Hence, the answer is the option (3).

Example 2: A constant power-delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :

1) $t^{2 / 3}$
2) $t$
3) $t^{3 / 2}$
4) $t^{1 / 2}$

Solution:

Power delivered by machine is, P

Force acting on the machine, F

\text { As we know, } P=\vec{F} \cdot \vec{V}

As force and velocity have the same direction the angle between force and velocity is 0^{\degree}

So $P=F V$
or $P=m a V=m \frac{d V}{d t} V$
Given that the machine is delivering constant power.
So $\mathrm{P}=\mathrm{C}$ (constant)
$P=C$
$F V=C$
$M \frac{d V}{d t} V=C$

Integrating both sides, we get

$\begin{aligned} & \quad \frac{V^2}{2} \propto t \\ & V \propto t^{1 / 2} \\ & \frac{d x}{d t} \propto t^{1 / 2} \\ & \begin{array}{l}\text { Again integrate both sides } \\ x \propto t^{3 / 2}\end{array}\end{aligned}$

Hence, the answer is the option(3).

Example 3: Sand is being dropped from a stationary dropper at a rate of $0.5 \mathrm{~kg}^{-1}$ on a conveyor belt moving with a velocity of $5 \mathrm{~ms}^{-1}$. The power needed to keep the belt moving with the same velocity will be :

1) 1.25 W
2) 2.5 W
3) 6.25 W
4) 12.5 W

Solution:

The power needed to keep the belt moving with the same velocity will be

$\begin{aligned} \mathrm{P} & =\left(\frac{\mathrm{dm}}{\mathrm{dt}}\right) \mathrm{v}^2 \\ & =(0.5) \times 25 \\ \mathrm{P} & =12.5 \mathrm{~W}\end{aligned}$

Hence, the answer is the option (4).

Example 4: A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n2 R t2 where n is a constant. The power delivered to the particle by the force acting on it is:

1) $M n^2 R^2 t$
2) $M n R^2 t$
3) $M n R^2 t^2$
4) $\frac{1}{2} M n^2 R^2 t^2$

Solution:

Centripetal acceleration, $a_c=n^2 r t^2$ where, $a_c=\frac{v^2}{r}$
$
\Rightarrow \frac{v^2}{r}=n^2 r t^2 \Rightarrow v=n r t \ldots
$
tangential acceleration, $a_t=\frac{d v}{d t}=n r \ldots$
Tangential force acting on the particle, $F=M a_t=M n r$
Power delivered, $P=\vec{F} \cdot \vec{v}=F v \cos \theta$
$
\therefore P=F v=(M n r) \times n r t\left(\because \theta=0^{\circ}\right) \Longrightarrow P=M n^2 r^2 t
$

Hence, the correct option is option 1.

Example 5: Sand is being dropped from a stationary dropper at a rate of $0.5 \mathrm{~kg}^{-1}$ on a conveyor belt moving with a velocity of $5 \mathrm{~ms}^{-1}$. The power needed to keep the belt moving with the same velocity will be :

1) 1.25 W
2) 2.5 W
3) 6.25 W
4) 12.5 W

Solution:

The power needed to keep the belt moving with the same velocity will be

$\begin{aligned} \mathrm{P} & =\left(\frac{\mathrm{dm}}{\mathrm{dt}}\right) \mathrm{v}^2 \\ & =(0.5) \times 25 \\ \mathrm{P} & =12.5 \mathrm{~W}\end{aligned}$

Hence, the answer is the option (4).

Conclusion

Power in physics is the rate at which work is done or energy is transferred, measured in watts (W), which is equivalent to one joule per second. It can be calculated as the product of voltage and current in electrical systems and as the rate of change of kinetic energy in mechanical systems. Power is crucial for efficiently operating various equipment and machines. Understanding power is essential for exams like JEE Main and NEET, where multiple questions are often asked on this concept.

Frequently Asked Questions (FAQs)

1. In terms of electricity, what is the difference between Power and energy?

The energy supplied by source in maintaining the flow of electric current is called electrical energy meanwhile the time rate at which electric energy is consumed by an electrical device is called electric power.

2. In terms of physics, what is power?

Power is a unit of measurement for the rate of energy transmission per unit of time. A scalar quantity is Power. In electrical engineering, Power refers to the rate at which electrical energy flows into or out of a given component.

3. What exactly is Power? What is the SI unit for it?

It is defined as the rate at which work is completed. The watt is a unit of measurement.

4. Define the term "average power."

Average power is the ratio of total effort or energy consumed to total time when a machine or person undertakes different quantities of work or utilizes energy at different periods of time.

5. What are Electric Generators?

Electric generators transform mechanical energy (the Power of motion) from an external source into electrical energy.

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A 500w carrier is modulated to depth of 80%. calculate total power in AM wave power in each side band, total power in side band

Hello,


To calculate the total power in the AM wave and power in each sideband, we can use the following formulas:


1. Total Power (Pt) = Carrier Power (Pc) x [1 + (μ^2)/2]


where μ is the modulation index (80% in this case)


1. Power in each sideband (Ps) = (μ^2/4) x Pc


Given:

Pc = 500 W (carrier power)

μ = 0.8 (modulation index)


Calculations:


1. Total Power (Pt) = 500 x [1 + (0.8^2)/2]

= 500 x [1 + 0.64/2]

= 500 x 1.32

= 660 W


2. Power in each sideband (Ps) = (0.8^2/4) x 500

= (0.64/4) x 500

= 0.16 x 500

= 80 W


So, the total power in the AM wave is 660 W, and the power in each sideband is 80 W.

Hope this helps,

Thank you

Read Complete Answer
Tanya Gupta 25 August,2024
i have -5.00 power glasses and also colour blind, can I get a job in airport ground staff??

Applying for a job as airport ground staff with -5.00 power glasses and color blindness presents specific challenges but is not necessarily a barrier if you meet certain conditions. Here's how these factors could impact your job prospects:

Vision Requirements:

  1. Eye Sight with Glasses: -5.00 power glasses indicate severe myopia (nearsightedness). Many airport ground staff roles require good vision for safety and operational efficiency. However, with corrective lenses, you may meet the visual acuity requirements, provided you pass the necessary eye tests. Ensure your glasses prescription is up-to-date and discuss your condition with prospective employers.

  2. Color Blindness: Color blindness can be a significant factor depending on the specific duties of the role. Ground staff positions often require distinguishing between different colors for tasks like identifying signals, reading colored indicators, or managing baggage. Some roles might be more lenient if your color blindness does not interfere with critical job functions, but others might be more stringent.

Job Assessment:

  1. Medical Examination: Most airport ground staff positions require passing a medical examination that assesses both vision and color discrimination. If your color blindness and vision can be managed with corrective lenses and do not impede job performance, you may still be considered.

  2. Job Specifications: Review job descriptions carefully to understand specific visual requirements. Certain roles might be better suited to your capabilities.

In summary, while there are challenges, it's possible to secure a ground staff position if your visual impairments can be managed effectively and do not compromise safety or job performance. Consult with potential employers about the specific requirements and consider roles that align with your abilities.

Read Complete Answer
monag2673 21 August,2024
My Gate score is 26.00 in 2024 exam. Now I am interested to take admission in COEP for M.tech in Power Electronics in year 2024-25.Cam I get this college or not ??

Hey there,

With a GATE score of 26.00 in the 2024 exam, getting admission to COEP (College of Engineering Pune) for M.Tech in Power Electronics might be challenging as the cutoff scores for COEP are typically higher. However, cutoffs can vary each year based on several factors, including the number of applicants and their scores. It is recommended to check the previous years' cutoffs for COEP and apply through the GATE counseling process to see if you can secure a spot.


But you can get other colleges. If you want to get a list of all possible colleges in which you can get admission at your GATE score then,

I would recommend you to use GATE college predictor tool by Careers360 to get the list of possible colleges you can get with your score.

Here is the link to the tool:

https://engineering.careers360.com/gate-college-predictor?utm_source=qna&utm_medium=ini-gate_cp

Click on the above link, fill the required details and you will get the list of possible colleges at your rank.


I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

Thank you and wishing you all the best for your bright future.

Read Complete Answer
kumardurgesh1802 02 August,2024
hlo , i am a student of aircraft maintenance engineering helicopter and power plant. mai janna chahta hu ki mere wale branch wale ka placement hota hai ki nhi

Hello Aman,

Aircraft Maintenance Engineering (AME) with a specialization in Helicopter and Power Plant is a highly specialized field with good placement opportunities. Here are some key points regarding placements for your branch:

Placement Opportunities for AME in Helicopter and Power Plant:

  1. Aviation Companies :

    • Companies like Air India, Indigo, SpiceJet, Vistara, and other domestic airlines regularly hire AMEs for maintenance and repair of their aircraft, including helicopters.

  2. Helicopter Operators :

    • Organizations such as Pawan Hans, Global Vectra Helicorp, and Heligo Charters operate fleets of helicopters and need qualified AMEs for maintenance.

  3. Maintenance, Repair, and Overhaul (MRO) Companies :

    • MRO companies such as Air Works, GMR Aero Technic, and Taneja Aerospace offer significant employment opportunities for AMEs.

  4. Government and Defense :

    • Organizations like Hindustan Aeronautics Limited (HAL), Indian Air Force, and other defense-related aviation sectors hire AMEs for the maintenance of their fleets.

  5. Private Charter Services :

    • Companies providing private charter services also require AMEs to ensure the safety and airworthiness of their aircraft.

  6. International Opportunities :

    • With the appropriate licenses and certifications, you can also find opportunities with international airlines and MRO companies.

How to Improve Placement Chances:

  1. Certifications and Licenses :

    • Obtain the necessary DGCA (Directorate General of Civil Aviation) licenses. The more licenses you have, the better your job prospects.
    • Consider additional certifications like EASA (European Union Aviation Safety Agency) or FAA (Federal Aviation Administration) licenses if you are looking at international opportunities.

  2. Internships and Practical Training :

    • Gain practical experience through internships or on-the-job training during your course. Many institutions have tie-ups with airlines and MRO companies for internships.

  3. Networking :

    • Attend industry seminars, job fairs, and conferences to network with professionals and companies in the aviation sector.

  4. Institutional Placement Support :

    • Utilize the placement cell of your educational institution. They often have industry contacts and can help you with job placements.

  5. Stay Updated :

    • Keep yourself updated with the latest technologies and developments in the aviation industry. Continuous learning and staying updated can give you an edge over others.

Key Companies and Organizations to Consider:

  • Domestic Airlines : Air India, Indigo, SpiceJet, Vistara, AirAsia India, etc.
  • Helicopter Operators : Pawan Hans, Global Vectra Helicorp, Heligo Charters, etc.
  • MRO Companies : Air Works, GMR Aero Technic, Taneja Aerospace, etc.
  • Government and Defense : Hindustan Aeronautics Limited (HAL), Indian Air Force, Indian Navy, etc.
  • Private Charters and Corporate Jets : Companies offering private and corporate jet services.

Conclusion:

Placements for AME specializing in Helicopter and Power Plant are promising, provided you have the necessary qualifications, practical experience, and certifications. Engaging with your institution's placement cell and networking within the industry can significantly enhance your job prospects.

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Asmee Biswas 21 July,2024

Question : In many organisations, the top management actively participates in making all decisions, while in some, even the lower levels of management have this authority. Because decision-making power is shared with lower levels, those levels are positioned close to the action. The statement "Decision making authority is shared with lower levels and is therefore located nearest to the points of action" highlights a management approach.

Option 1: Authority

Option 2: Delegation

Option 3: Accountability

Option 4: Decentralisation

Correct Answer: Decentralisation


Solution : Decentralization is a type of organisational structure in which the top management delegated power to the middle and lower levels of management in an organisation. Hence, the correct option is 4.

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Team Careers360 26 January,2024
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