Watts Law: What is it? Formula, Examples & Watt’s Law Triangle

What Is Watts Law

What is Watts Law?

Watt’s law defines the relationship between power, amperage, and voltage drop in an electrical circuit. Watts Law also states that the power of an electrical circuit is the product of its voltage and current.

Watts Law Formula

The formula for Watts law can be given as follows. It gives the relationships between power (watts), current (amps) and voltage(volt)

    \begin{align*} Power = Voltage\times Current\end{align*}

    \begin{align*}Voltage = \frac{Power}{Current} \end{align*}

    \begin{align*}Current = \frac{Power}{Voltage} \end{align*}

Watts Law Examples

Below we will go over some examples to better explain Watt’s law.

Watts Law Example 1

Suppose you were trying to find out how many 500-watt lighting devices you could plug into a circuit without blowing a fuse.

First, you’d like to know how much current can be drawn from the circuit. Most homes have 15A circuits and most of the circuits have a circuit breaker off of 20A. So, what would be the total power?

We know that Watts = Volts x Amps. So, here voltage and current values are given as 110V and 20A. Now, the calculated Watts would be 2200W. So whatever we plug into our circuit must be less than 2200 watts, since that’s all the power available on this circuit. You could safely plug four 500-watt lights into the circuit (or two 1000watt lights) with a 200 Watt as a safety margin.

Watts Law Example 2

If the light bulb voltage is 120 volts and the power is 60 watts, what really is the current?

So, here the voltage and power of a bulb are given as 120V and 60W respectively. We already know current = Power / Voltage. So, on substituting the values, the value of current would be 0.5 Amperes.

Watts Law Example 3

Consider your home’s 100 Watt light bulb. We know that the voltage applied to the bulb is usually 110V or 220V so that the current consumed can be measured as follows.

I = P/V = 100W / 110V = 0.91 Amps or I = P/V = 100W / 220V = 0.45 Amps.

But you can see that it’s easier to use a 60W light bulb. Your electrical provider would usually bill you for use in Kilo-Watt Hours (kWh). One kWh is the amount of energy required to do 1000 watts of energy for one hour.

Watts Law Vs. Ohms Law

Watt’s Law says the relationship between power, voltage and current.

Power: Power is the rate at which energy is being used. The unit of measurement for electrical power is called the Watt, named after James Watt. Whenever one Volt is used to move an Ampere through a circuit, the work done is equal to one Watt of power.

    \begin{align*} P = V \times I\end{align*}

As electrons pass across a resistance in an electrical circuit, the electrons collide with each other and the atoms that make up the resistance. These collisions produce heat and result in a loss of energy. Hence a variation in watts law is given as

    \begin{align*}P = I^{2}R\end{align*}

Current: The movement of electrons or other particles through a conductor is known as current. The unit used to calculate the current parameter is the Ampere. The symbol used to represent the amplifier is the letter “A.” The upper and lower cases are used depending on the situation. The symbol used to represent the current parameter is the letter “I.”

Voltage: The electrical pressure that causes electrons or other particles to move through a circuit is known as Voltage. The unit used to calculate the voltage parameter is the volt. The symbol used to represent the volt is the letter “V.” Both the upper case and the lower case are used depending on the situation.

Resistance: It is a measure of the resistance to the current flow in the electrical circuit. Resistance is measured by ohms, symbolised by the Greek letter omega. Resistance is also good because it gives us a way to shield ourselves from the harmful energy of electricity.

Ohm’s Law affirms the relationship between voltage, current and resistance.

The Ohm’s law can be represented as:

    \begin{align*} V = I \times R \end{align*}

    \begin{align*}I = V/R \end{align*}

    \begin{align*}R = V/I \end{align*}

Ohms Law Pie Chart
Ohms Law Pie Chart

Watts Law Triangle

Since both laws use the same electrical quantities, they can be combined to come up with some useful equations. The basic Ohms Law equation is transposed for power. It gives us some combinations of the same equation to find the various individual quantities.

Power Triangle
Power Triangle

There are three possible formulas for calculating electrical power in a circuit. If the calculated power is positive, it means the equipment is consuming or using power. But if the calculated power is negative in value the component produces or generates power.

Power Triangle Values
Values calculated from Power Triangle

Applications of Watts law

Some of the applications of Watt’s law include:

  • If you have a power source, you would use this formula to measure the actual power which the source can produce. You could use it to measure the power requirement for just one component. When the current and the voltage of the source are given, the values can be multiplied.
  • The power requirement of a building can be measured using the Watt formula. It is important to estimate the total power requirement when designing the wiring of a building. You can then use this knowledge to decide the appropriate wire sizes for the house. You may also measure the cost of electricity. The power requirement of the building is accomplished by measuring and adding up the individual power rating of each electrical device or part of the building.
  • If you know the power and voltage of the electrical component, you can measure the current using the Watt formula (I = P / V). The same is true for voltage when only current and power (V = P / I) are understood.
  • The formulas obtained from the combination of Watt’s law and Ohm’s law can be applied to determine the electrical resistance of a component.
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About Vidya Muthukrishnan

Vidya Muthukrishnan is currently employed as a Senior Engineer in a product based IT company. She has 5 years of professional teaching experience, previously Assistant Professor in the Department of Instrumentation and Control Engineering at the Sri Krishna College of Technology. She also has 1 year of industry experience with TCS, India. Vidya completed her B.Tech Electronics and Instrumentation from SASTRA University and M.Tech in Biomedical Engineering from VIT University Vellore.