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

Contents

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Key learnings:

Watts Law Definition: Watts Law is defined as the relationship between power, voltage, and current in an electrical circuit.
Watts Law Formula: The formula for Watts Law includes power equals voltage multiplied by current, voltage equals power divided by current, and current equals power divided by voltage.
Practical Examples: Practical examples of Watts Law include calculating power usage in household circuits and determining current for light bulbs.
Power Triangle: The Watts Law Triangle combines formulas to find power, voltage, and current in a circuit.
Applications: Watts Law helps measure power requirements for buildings and electrical components, ensuring safe and efficient designs.

What is Watts Law?

Watts Law states the relationship between power, current and voltage drop in an electrical circuit. Instantaneous electric power is the product of voltage and current. For DC, or for AC when voltage and current are in phase, the same product gives the average power in watts.

Watts Law Formula

The Watts law formulas below relate power in watts, current in amperes and voltage in volts:

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

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

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

Watts Law Examples

The examples below apply those formulas.

Watts Law Example 1

Suppose you want to know how many 500-watt lamps a branch circuit can supply before the breaker trips.

First find the current the circuit is allowed to carry. In many North American homes, lighting and receptacle circuits are 15 A or 20 A. This example uses a 20 A breaker and a 110 V supply, which is an older nominal value near today’s 120 V. What raw power does P = V I give?

Watts = volts x amps. With 110 V and 20 A the product is 2200 W. Four 500 W lamps draw 2000 W and leave a 200 W gap under that raw product. That arithmetic is not a wiring design. In the US, NEC 210.20(A) requires a standard breaker to be sized for continuous load plus 25 percent, so a load that stays on for three hours or more is kept at or below 80 percent of the breaker rating. Four 500 W lamps on a 20 A, 110 V circuit would exceed that continuous-load limit.

Watts Law Example 2

If a lamp is rated 120 volts and 60 watts, what current does P / V give?

With 120 V and 60 W, I = P / V = 0.5 A. That is the rated current of a 60 W incandescent lamp. An LED lamp of the same light output draws much less.

Watts Law Example 3

Take a 100 W lamp. On a 110 V supply or a 220 V supply the current is:

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

A 60 W lamp draws less current and uses less energy than a 100 W lamp on the same voltage. Utilities usually bill energy in kilowatt-hours (kWh). One kWh is 1000 watts of power used for one hour.

Watts Law Vs. Ohms Law

Watt’s Law relates power, voltage and current. Ohm’s Law relates voltage, current and resistance.

Power: Power is the rate at which energy is converted. The SI unit is the watt, named after James Watt. One volt driving one ampere delivers one watt.

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

When charge moves through a resistance, collisions convert electrical energy to heat. Combining Watts Law with Ohm’s Law then gives

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

Current: Current is the movement of charge through a conductor. The SI unit is the ampere, symbol A. The quantity itself is usually written I.

Voltage: Voltage is the electric potential difference that drives charge around a circuit. The SI unit is the volt, symbol V.

Resistance: Resistance measures how strongly a circuit opposes current. The unit is the ohm, symbol omega. Designers use resistance to set current, drop voltage and convert energy to heat. Insulation, not resistance alone, is what keeps a person from contacting live parts.

Ohm’s Law states the relationship between voltage, current and resistance for an ohmic conductor.

Ohm’s Law can be written as:

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

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

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

Watts Law Triangle

Because both laws use V, I and R, they can be combined. Substituting Ohm’s Law into P = V I gives the other two power forms shown on the triangle: P = I squared R and P = V squared / R.

Those three power formulas describe magnitude. Sign is a convention: a positive result is often taken as power absorbed by a load, and a negative result as power delivered by a source.

Power Triangle Values — Values calculated from Power Triangle

Applications of Watts law

Watt’s Law is used to:

Find the power a source can deliver, or the power one component draws, by multiplying the voltage and current at that point.
Estimate a building load by adding the watt ratings of the connected equipment, then convert to current with I = P / V when you size supply and branch circuits. Wire size, breaker rating and energy cost still need the local wiring rules and the utility tariff. The formula alone does not finish a design.
Find current from I = P / V when power and voltage are known, or find voltage from V = P / I when power and current are known.
Combined with Ohm’s Law, the same quantities can be rearranged to find resistance, for example R = V / I or R = P / I squared.