Power Formula: Explained with Solved Examples
Power is a measure of how quickly work is performed or energy is transferred. It is usually defined as the amount of work accomplished or energy transmitted over a specific period. The power formula is used to determine the rate at which work is being carried out by a system or object. Power is highly useful as it indicates the amount of force needed to move an object and set it into motion. Once this threshold is surpassed, the object continues moving until acted upon by an external force.
What is Power?
Power is the rate at which work is done or energy is transferred over time. It quantifies how quickly energy is used or work is performed in a system.
Mathematically, power is defined as the amount of work done or energy transferred divided by the time it takes.
It is expressed in units of watts (W) in the International System of Units (SI), where 1 watt equals 1 joule of energy per second.
Power plays a crucial role in understanding and analysing the efficiency and performance of systems, such as machines, electrical devices, and physical movements.
Formula of Power or Power Equations
Power = Work / Time
Where:
Power (P): The rate at which work is done, measured in watts (W).
Work (W): The total amount of work done, measured in joules (J).
Time (t): The time taken to do the work, measured in seconds (s).
Alternative Forms of the Power Formula
In terms of force and velocity:
$P = F \cdot v$
Where:F: Force applied (in newtons, N).
v: Velocity of the object (in meters per second, m/s).
In electrical systems:
$P = V \cdot I$
Where:
V: Voltage (in volts, V).
I: Current (in amperes, A).
For resistive circuits:
$P = I^2 \cdot R \quad \text{or} \quad P = \dfrac{V^2}{R}$
Where:R: Resistance (in ohms, Ω).
Power Formula Solved Examples
Example 1: Work and Time
Problem: A person does 200 joules of work in 10 seconds. What is the power?
Solution:
$P = \dfrac{W}{t}$
$P = \dfrac{200 \, \text{J}}{10 \, \text{s}} = 20 \, \text{W}$
Answer: The power is 20 watts.
Example 2: Force and Velocity
Problem: A car engine applies a constant force of 500 N to move a car at a velocity of 10 m/s. What is the power of the engine?
Solution:
$P = F \cdot v$
$P = 500 \, \text{N} \cdot 10 \, \text{m/s} = 5000 \, \text{W}$
Answer: The power is 5000 watts (5 kW).
Example 3: Electrical Power
Problem: An electric bulb operates at 220 V and draws a current of 0.5 A. What is the power consumption of the bulb?
Solution:
$P = V \cdot I$
$P = 220 \, \text{V} \cdot 0.5 \, \text{A} = 110 \, \text{W}$
Answer: The power consumption is 110 watts.
Example 4: Electrical Resistance
Problem: A resistor has a resistance of 10 Ω, and the current flowing through it is 2 A. What is the power dissipated by the resistor?
Solution:
$P = I^2 \cdot R$
P = $(2 \, \text{A})^2 \cdot 10 \, \Omega = 4 \cdot 10 = 40 \, \text{W}$
Answer: The power dissipated is 40 watts.
Example 5: Work Done by a Machine
Problem: A machine does 5000 joules of work in 25 seconds. Calculate its power output.
Solution:
$P = \dfrac{W}{t}$
$P = \frac{5000 \, \text{J}}{25 \, \text{s}} = 200 \, \text{W}$
Answer: The machine's power output is 200 watts.
FAQs on Power Formula
1. What are the 3 formulas for power?
In terms of work and time:
$P = \dfrac{W}{t}$
Where:P is power (in watts, W),
W is work done (in joules, J),
t is time (in seconds, s).
In terms of force and velocity:
$P = F \cdot v$
Where:P is power (in watts, W),
F is force (in newtons, N),
v is velocity (in meters per second, m/s).
In electrical systems:
P=V⋅I
Where:P is power (in watts, W),
V is voltage (in volts, V),
I is current (in amperes, A).
2. What is the power P formula?
The most basic formula for power is:
$P = \dfrac{W}{t}$
This formula calculates power as the rate at which work (W) is done over time (t).
For specific contexts, the formula adapts:
Mechanical systems: P=F⋅v
Electrical systems: P=V⋅I
3. What is power and its unit?
Power is the rate at which work is done or energy is transferred over time. It quantifies how fast energy is being used or delivered in a system.
Unit of power (SI): Watt (W), where $1 \, \text{W} = 1 \, \text{J/s}$.
Larger units include kilowatt (1 kW=1000 W) and horsepower (1 hp=746 W).
4. How to Find Power in Physics?
To find power in physics, use the appropriate formula based on the context of the problem. Power is the rate at which work is done or energy is transferred, and it can be calculated using one of the following equations:
5. What Is the Equation for Power?
General Formula (Work and Time):
$P = \dfrac{W}{t}$
Where:
P: Power (in watts, W)
W: Work done (in joules, J)
t: Time taken (in seconds, s)
6. What is the formula for power in mechanical systems?
In mechanical systems, power is often calculated using the formula:
P=F⋅v
Where:
P is power (in watts, W),
F is force (in newtons, N),
v is velocity (in meters per second, m/s).
This formula calculates the power as the product of force and the velocity at which the force is applied.
7. What is the formula for power in electrical systems?
In electrical systems, power is calculated using:
P=V⋅I
Where:
P is power (in watts, W),
V is voltage (in volts, V),
I is current (in amperes, A).
This formula determines the power consumed or delivered by an electrical device based on the voltage and current in the circuit.
8. What are the units of power?
The SI unit of power is the watt (W), which is defined as one joule per second (1 W = 1 J/s).
Larger units of power include:
Kilowatt (kW): 1 kW = 1000 W
Horsepower (hp): 1 hp = 746 W
9. How do you calculate power in a rotating system?
In a rotating system, power can be calculated using the formula:
P=τ⋅ω
Where:
P is power (in watts, W),
τ is torque (in newton-meters, Nm),
ω is the angular velocity (in radians per second, rad/s).
This formula is used for calculating the rotational power in systems such as motors or engines.
10. What is the relationship between power and efficiency?
Power is related to efficiency in terms of how much input energy is converted into useful output energy. The formula for efficiency (ηηη) is:
$η = \dfrac{\text{Useful Power Output}}{\text{Total Power Input}} \times 100$
Where:
η is efficiency (in percentage),
Useful Power Output is the power converted into useful work (in watts),
Total Power Input is the total energy supplied to the system (in watts).
