Power Formula 

What is Power?

Power is a fundamental concept in physics that represents the rate at which work is done or energy is transferred or transformed. It measures how quickly or efficiently a task is performed. Power is closely related to both work and energy.

Work is defined as the transfer of energy that occurs when a force acts upon an object to cause its displacement. Power, on the other hand, quantifies how quickly that work is done. In other words, power is the amount of work done per unit of time.

Formula of Power

The formula for calculating power is:

Power (P) = Work (W) / Time (t)

Where:

Power (P): is measured in watts (W),

Work (W): is measured in joules (J),

Time (t): is measured in seconds (s).

Watt (W): is defined as one joule (J) of work done or energy transferred per second (s). Therefore, if one joule of work is done in one second, the power is one watt.

Power is a crucial concept in various fields and applications. In electrical systems, power is used to measure the rate at which electrical energy is generated or consumed. In mechanical systems, power is used to quantify the rate at which work is performed, such as the power output of an engine or motor. Power is also important in understanding the efficiency of systems and devices, as higher power indicates a faster rate of energy transfer or work done.

Solved Examples on Power Formula

Example 1: A motor does 5000 joules of work in 10 seconds. Calculate the power generated by the motor.

Solution:

Given:

Work (W) = 5000 J

Time (t) = 10 s

Using the formula for power:

Power (P) = Work (W) / Time (t)

Substituting the given values:

P = 5000 J / 10 s

P = 500 W

Therefore, the power generated by the motor is 500 watts.

Example 2: A car engine exerts a force of 1500 Newtons to push the car a distance of 50 meters in 10 seconds. Calculate the power developed by the engine.

Solution:

Given:

Force (F) = 1500 N

Distance (d) = 50 m

Time (t) = 10 s

To calculate power, we need to find the work done by the engine. Work (W) is given by the formula:

Work (W) = Force (F) × Distance (d)

So, the work done by the engine is:

W = F × d

W = 1500 N × 50 m

W = 75,000 J

Now, we can calculate power using the formula:

Power (P) = Work (W) / Time (t)

Substituting the given values:

P = 75,000 J / 10 s

P = 7,500 W

Therefore, the power developed by the car engine is 7,500 watts.

Power Formula in Different Terms

Understanding how power is calculated helps in analyzing and optimizing performance in these different terms:

Power Formula in Terms of Energy

The power formula in terms of energy is used to determine how quickly energy is transferred or converted over time. The formula is:

P = E/t

where:

• P is power
• E is energy
• t is time

Power Formula in Terms of Force

The power formula with force is:

P = F.v

Derivation:

• Definition of Power: Power (P) is the rate at which work (W) is done over time (t). P = W / t
• Work Done by Force: Work (W) is defined as the force (F) applied on an object multiplied by the distance (d) moved by the object in the direction of the force.W = F · d
• Combining Both Equations: Substitute the expression for work into the power formula: P = F · d / t
• Relating Distance and Velocity: Distance (d) divided by time (t) gives the velocity (v) of the object. v = d / t
• Final Formula: Substitute velocity (v) into the power equation: P = F · v

Power Formula in Terms of Torque

In rotational systems, power can be expressed in terms of torque using the formula P = τ · ω

Here,

• 𝑃 represents power,
• τ (tau) is the torque applied, and
• ω (omega) is the angular velocity.

Derivation:

• Definition of Power:Power (P) is the rate at which work (W) is done over time (t).P = W / t
• Work Done by Torque:Work (W) in a rotational system is the torque (τ) multiplied by the angular displacement (θ).W = τ · θ
• Combining Both Equations:Substitute the expression for work into the power formula:P = τ · θ / t
• Relating Angular Displacement and Angular Velocity:Angular displacement (θ) divided by time (t) gives the angular velocity (ω).ω = θ / t
• Final Formula:Substitute angular velocity (ω) into the power equation:P = τ · ω

Power Formula in Ray Optics

Power formula in Ray Optics is P = 1 / f. Here P is the power of the lens measured in diopters (D), and 𝑓 is the focal length of the lens in meters.

Power Formula in Electricity

In electricity, power is calculated using the formula P = V · I, where 𝑃 represents power in watts (W), 𝑉 is voltage in volts (V), and 𝐼 is current in amperes (A).

Derivation of Power Formula in Electricity:

• Definition of Power: Power (P) in an electrical circuit is the rate at which electrical energy is consumed or converted into another form. P = W / t
• Electrical Work Done: Electrical work (W) is the product of voltage (V) and charge (Q). W = V · Q
• Relating Charge and Current: Current (I) is the rate of flow of charge (Q) over time (t). I = Q / t
• Combining Both Equations: Substitute the expression for work into the power formula: P = V · Q / t
• Final Formula: Since I = Q / t, substitute I into the power equation: P = V · I

FAQ’s on Power formula:

What is power?

Power is the rate at which work is done or energy is transferred or transformed. It measures how quickly or efficiently a task is performed.

What is the SI unit of power?

The SI unit of power is the watt (W).

How is power calculated?

Power is calculated by dividing the work done or energy transferred by the time taken. The formula for power is: Power (P) = Work (W) / Time (t).

What is the difference between power and energy?

Energy is the total amount of work done or the capacity to do work, while power is the rate at which that work is done or energy is transferred.

What is the relationship between power and time?

Power is inversely proportional to time. As the time taken to perform a task decreases, the power required to perform the task increases.

What is the difference between power and torque?

Power and torque are related but distinct concepts. Power is the rate at which work is done, while torque is the rotational force applied to an object.

Can power be negative?

Power can be negative if work is being done on the system or energy is being transferred in the opposite direction. Negative power indicates power absorption or consumption.

What is electrical power?

Electrical power refers to the rate at which electrical energy is consumed or produced. It is commonly measured in watts and used to quantify the energy usage of electrical devices.