After learning about electrical voltage and electrical current, we still need to learn the last element of an electrical circuit. We still need to learn the electric power formula to solve all the electrical phenomena.
Electric Power Formula
How much the power is absorbed by a circuit element depends on the capability of the said element and the energy supplied to the circuit. An 120 watt bulb compared to a 60 watt bulb will shine brighter. Not only how better it performs, our electrical bill is also calculated based on our power consumption.
The more “watt” we use, the more bills we need to pay. We will use a DC circuit right now.
Based on this basic explanation, the circuit analysis of power and energy are not less important than voltage and current.
The relationship between power and energy to voltage and current can be stated as:
Power is the time rate of generating or absorbing energy, measured in watts (W)
The statement above can be expressed in mathematical equation as:
Where:
p = power, measured in watts (W)
w = energy, measured in joules (J)
t = time, measured in seconds (s)
In another way, electric power is the rate of electrical energy (w) transferred by an electrical circuit per unit of time (t).
Combining the equation above with the equation of voltage and equation of current, we will get the electric power formula:
P = V × I
From the equation above we can simply conclude that the electric power is the multiplication of electric voltage measured in volts (V) and the electric current measured in ampere (A). Electricity power here can be measured by V x A or volt x ampere aside from watt.
The difference of volt-ampere and watt will be explained in detail in another lesson.
The equation above is called instantaneous power. If it has a positive (+) sign, it means the power is delivered to an element or the element is absorbing power. If it has negative (-) sign, it means the power is being supplied by the element. We can understand this after observing the illustration below.
Power Absorbed and Delivered
There is another easy way to determine the sign of power, by determining the direction of current and voltage first.
Observe the illustration below.
The illustration above shows us how to get a positive sign. This is widely known as the passive sign convention.
In the illustration above, the current is entering the positive polarity of voltage, it makes the power p = +vi or p > 0 implies that the element is absorbing power and the absorbed power formula is p = vi.
Opposite of that, observe the illustration below.
The illustration above tells us that the element is supplying power since the current is leaving the element at the positive polarity (think of it as a battery, it shares the same illustration).
In the illustration above, the current is leaving the positive polarity of voltage, it makes the power p = -vi or p < 0 implies that the element is delivering power and the delivered power formula is p = -vi.
Passive sign convention is achieved when the current enters through the positive terminal of an element and p = +vi, if the current enters the negative terminal, p = -vi
Electrical Energy and Power Equation
For all the illustrations shown above, we can conclude that:
(+) power absorbed is equal to (-) power supplied
Because absorbing -12W power is equal to supplying +12W power.
This is another approach to prove that the law of conservation of energy will always be obeyed by any electrical circuit. The mathematical equation itself is:
From the equation above it is clear that the total power supplied must balance the total power absorbed.
When calculating energy in a specific period of time, we can use:
The electric power utility measure their energy in watt-hours (Wh) where:
1 Wh = 3.600 Joules
Electric Power Formula Examples
For better understanding, let us review some examples below:
1. An energy source generates a constant current of 2 A for 10s to turn on a light bulb. If 2,3 kJ is used to produce light and heat, how much voltage drop for the bulb?
Answer:
The total charges is
The voltage drop is
2. Calculate the power delivered to an element at t = 3 ms if the current is entering at the positive terminal.
The current is
i = 5 cos 60 π t A
The voltage is
(a) v = 3i, and
(b) v = 3 di/dt
Answer:
Let’s start with voltage(a) first.
Hence, the power is
At t = 3 ms,
Now we will proceed to voltage(b)
Hence, the power is
At t = 3 ms,
3. Imagine we have a simple electrical circuit with a resistor and a voltage source. The power measured across the resistor is 10 watt while the voltage source is 5 volts. Calculate the current flowing in the circuit and the resistance of the resistor.
Answer:
We can easily solve this with
Since we have the voltage and the current, we can easily find the resistance with Ohm’s Law. But here we will involve the power.
Since,
Frequently Asked Questions
What are the 3 formulas for electric power?
In order to calculate the electric power in a circuit, we can use:
P = V I
P = V^2 / R
P = I^2 R
How do you calculate electric power?
The easiest way to calculate electric power is by multiplication of voltage and current, and it is expressed as P = V I. Where P is electric power, V is electric voltage, I is electric current.
What is electric power and its unit?
Electric power is the rate of electrical energy (w) transferred by an electrical circuit per unit of time (t).