# Power Formula

#### Physics Formulas

Most things around us require some power to function effectively. Here the word power refers to anything that provides the necessary force or energy for something to work correctly. For example, many devices like mobile phones, computers, fans, etc., run on electricity; if we do not charge our phone battery, it will turn off. Similarly, if there is no electricity in the home, the fan cannot work. The energy for such devices is, therefore, electricity. This power can also be in other forms, such as physical or human resources.

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## What is Power?

The capacity to do particular work is known as Energy. The Energy expended to do work in unit time is termed Power. It is represented as P.

### Formula for Power

**P = F × s/t**

As we know,

Power = Work done upon time

**P = w/t**

Work = Force ( F ) × Displacement(s)

**P = F × s/t**

Here,

P = Power.

F = Force applied on the body.

W = Work done by the body.

t = Total time taken.

s = Total displacement of the body.

### Advantages of Power formula

The power formula gives many benefits, such as

- Power formula helps us determine the work done by a particular object or person at a specific time.
- It helps to determine which object is more efficient and which is less efficient. For example, if x and y are doing the same task and x completes it in 3 hours while y completes the same task in 6 hours. This means that "x" is more efficient than "y." This is simply because x has more power than y.
- From the example, one can also understand how power can help determine how much work is done and at what time. And knowing the efficiency of someone or something's work, we can also make good judgments and decisions about it.

### Power Formula for Different Relations

**P = VI**

The formula was derived by a great scientist named Ohm, and this formula is named after him and is also known as Ohm's law.

Where,

P = Power,

V = Potential difference

I = Current.

**Electric Power Formula**

**P = R × I ^{2} or V^{2}/ R **

The above formulas are a variant of Ohm's law.

Where,

R = resistance

V= potential difference

I = current.

**Power Equation**

**P = E/t**

This formula is also known as the mechanical power equation.

Where,

E = Energy in joule

t = time

**P = w/t**

This formula is derived from the theorem of work-energy

Where,

W = work in joule

t = Time

**P = F × s/t**

In this formula, F = force applied to the object, s = displacement of the object, and t = total time taken.

### Solved Examples

**Q1. An electric machine uses 200 J of energy to do work in 10s. How much power does it use?**

**Ans.** Work done = W = 300 J,

Time taken t = 10 s.

Power used by it is given by

P = W/T

P = 200 / 10

P = 20 Watts

**Q2. Ram has a mass of 60 kg and runs up to 12m high in 40 seconds. Calculate his power.**

**Ans.** Given, m (mass) = 60 kg,

h (Height) = 12 m,

t (time taken) = 40 seconds.

Power is given by:

P = W / T

P= mgh / t

P = 60 x 9.8 x 12 / 40

P = 588 Watts

### Frequently Asked Question (FAQs)

**Q1. What is the formula of Power?**

**Ans.** P = W / t

Where W = Work Done

t = time

**Q2. What is the SI unit for Power?**

**Ans.** Watt (W).

**Q3. Can Power be negative?**

**Ans.** The Power represents the rate of electrical energy flowing out or into an electrical device or control volume. It is a signed quantity; negative Power represents Power flowing in the opposite direction from positive Power.

**Q4. How is force related to Power?**

**Ans.** In the linear cases where a constant force moves an object at a constant velocity, the Power is just P = Fv. In a normal case, velocity direction is not the same as the force, then the velocity and scalar product of force must be used.

**Q5. Is power is a vector quantity?**

**Ans.** Power is a scalar quantity.