# Power Formula

## Power Formula

The capacity to conduct work is known as energy. Power is defined as the amount of energy used to accomplish work in a unit of time. It is abbreviated as P.

Power Formula is stated as follows:

P=Wt

Where P is the power.

W is the work done by a body.

t is the time duration in which work gets done.

### Benefits of Power Formula

The Power Formula has a variety of uses, including:

• The Power Formula aids in calculating the amount of work performed by a specific object or person at a specific time.
• This information is useful in identifying which objects are more and less efficient. For instance, if two people, x and y, are performing the same task, x completes it in four hours while y completes it in six. It implies that “x” is more effective than “y”. The reason is simple: x has more power than y.
• From the provided example, it is also clear how power can be used to estimate how much work has been completed and when. We can also make wise judgments and decisions about something or someone if we are aware of how effectively they work.

### A Brief Overview Of The Power Formulas

• In layman’s terms, the power of anything can be calculated by dividing the amount of work it has completed by the amount of time it has taken. This is the general concept of power; the formula can vary in many situations.
• One Power Formula is known as “Ohm’s law,” after the scientist who first proposed it. The electricity chapter of the book contains the Power Formula; P = VI. P stands for power, V for potential difference, and I for current in the equation P = VI.
• The mechanical Power Formula, is a further formula. P = E/t is the equation, where P stands for power, E for energy, and t for time in seconds. According to this equation, power is defined as the amount of energy consumed per unit of time.

Power is calculated as Work Done by the Object or Body / Total Time. The Power Formula varies depending on the necessary statements. Both force-related objects and electronic devices may have a different effect.

### The Power Formula for Different Relations and Units are:

P=VI

This Power Formula is taken from the chapter on electricity. Ohm, a famous scientist, provided the formula, which bears his name and is also referred to as Ohm’s law.

According to this, power is inversely correlated with conductor potential difference. P stands for power, V for potential difference, and I for current in this context. The watt is the SI unit. For I, the unit is in the column, while for V, it is in the volt.

Electric Power Formula

$$P = R × I_2 or V_2/ R$$

This Power Formula is a special case of Ohm’s law. Here, the letters R, V, and I stand for resistance, potential difference, and current, respectively.

According to this, power is inversely proportional to the resistance provided by the conductor and directly proportional to the square of the potential difference.

Power Equation

P = E/t:

The mechanical Power Formula is another name for this equation. Here, E denotes energy in joules, and t denotes seconds of time. According to this equation, power is defined as the amount of energy consumed per unit of time.

P = w/t

The most typical and fundamental Power Formula that we learn about early on is this one. The work-energy theorem is the source of this formula. It says that power is the amount of work done in a given amount of time. Here, W denotes work in joules, and t denotes seconds of time.

P = F × s/t

F stands for the force applied in this Power Formula. The object’s displacement is indicated by the letter s, and the amount of time is indicated by the letter t. According to this definition, power is the total amount of time it takes an object to move from one location to another when an external force is applied to it. As was already mentioned, the power equation differs for various fields, but its essence is essentially the same across the board.

### NCERT Topic Wise Solutions for all the Classes

Derivation of some Power Formula are as below:

Electric Power:

As we know from Ohm’s law:

V = IR

I = V / R

Now putting this value in a standard equation, P = VI

We get,

P = I × I × R

P = I^2 × R

Or,

P = V × V / R

P = V2 / R.  (hence proved)

Here,

P = Power of the object or body.

V = Potential Difference between two ends of a conductor.

I = current flowing through the circuit.

R = Resistance offered by the wire.

Power Formula

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.

### Solved Examples

Example 1: A mobile phone’s battery works at 12.0 V and requires to provide a current of 0.9 A whenever music plays. How much power will be required for the same?

Solution: The Power required from the battery can be found by applying the electric Power Formula.

Thus, P = VI

P = (12.0 V) (0.9 A)

P = (12.0 J/C) (0.9 C/s)

P = 10.8 J/s

P = 10.8 W

Hence, the power required by the battery of the mobile phone is 10.8 W.

Example 2: An electrical circuit consists of resistance 3Ω and a current 4A flowing through it. Calculate the power.

Solution:

I = 4A & R = 3Ω

Electric Power Formula= P = (I^2)R

P = 42×3

P = 16×3 = 48 Watts