An rate at which the work is being done in an electrical circuit is called an electric power. In other words, the electric power is defined as the rate of the transferred of energy. The electric power is produced by the generator and can also be supplied by the electrical batteries. It gives a low entropy form of energy which is carried over long distance and also it is converted into various other forms of energy like motion, heat energy, etc.
Definition
Electric power is the rate at which work is done or energy is transformed into an electrical circuit. Simply put, it is a measure of how much energy is used in a span of time.
Symbol |
P |
SI Unit |
Watts, joule per second |
Scalar or Vector |
Scalar Quantity |
Formula |
P=VI |
Electric Power Formula
The formula for electric power is given by
P = VI |
where,
P is the power
V is the potential difference in the circuit
I is the electric current
Power can also be written as
P = I^{2}R |
P = V^{2}/ R |
The above two expressions are got by using Ohms law, Where, Voltage, current, and resistance are related by the following relation
V = IR
Where,
- R is the resistance in the circuit.
- V is the potential difference in the circuit
- I is the electric current
Power Energy Formula
Since power is the rate of energy consumption, energy can directly be calculated using
Where,
E is the energy consumption (in Joules)
t is the time in seconds
Where,
- Q is the charge (in Coulombs)
- V is Potential difference in volts
- t is the time in seconds
Types of an Electric Power
The electrical power is mainly classified into two types. They are the DC power and the AC power.
1. DC Power
The DC power is defined as the product of the voltage and current. It is produced by the fuel cell, battery and generator.
Where,
P – Power in watt.
V – voltage in volts.
I – current in amps.
2. AC Power
The AC power is mainly classified into three types. They are the apparent power, active power and real power.
- Apparent Power –The apparent power is the useless power or idle power. It is represented by the symbol S, and their SI unit is volt-amp.
Where,
S – apparent power
V_{rms} – RMS voltage = V_{peak}√2 in volt.
I_{rms} – RMS current = I_{peak}√2 in the amp.
- Active Power –The active power (P) is the real power which is dissipated in the circuit resistance.
Where,
P – the real power in watts.
V_{rms} – RMS voltage = V_{peak}√2 in volts.
I_{rms} – RMS current = I_{peak}√2 in the amp.
Φ – impedance phase angle between voltage and current.
- Reactive Power –The power developed in the circuit reactance is called reactive power (Q). It is measured in volt-ampere reactive.
Where,
Q – the reactive power in watts.
V_{rms} – RMS voltage = V_{peak}√2 in volt.
I_{rms} – RMS current = I_{peak}√2 in the amp.
Φ – impedance phase angle between voltage and current.
The relation between the apparent, active and reactive power is shown below.
The ratio of the real to the apparent power is called power factor, and their value lies between 0 and 1.
Problems
Based on the information given above try the application problem given below:
Example:
A 9V battery is connected to a resistor having a resistance of 10 Ω. What is the current and power across the resistor?
Solution:
I = V/R = 9/100 = 0.9 A
P = VI = 9 × 0.9 = 8.1 J/s or 8.1 W