Calculating Ohm’s Law and Power in Circuits

The way in which voltage (V), current (I), and resistance (R) interact in any DC circuit was first explained by German physicist Georg Ohm.

In the field of electricity, German physicist Georg Ohm discovered a key principle, he found that at a consistent temperature, the flow of electric current through a fixed, unchanging resistance is directly proportional to the voltage applied across it.

However he also found that the current is inversely proportional to the resistance itself.

This fundamental relationship between voltage, current, and resistance forms the cornerstone of Ohm’s Law, that can be expressed mathematically as shown below.

• Current (I) = Voltage (V) / Resistance (R)
• The result will be in Amperes (I)

If we already know two values of voltage, current, or resistance, we may use Ohm’s Law to get the remaining one.

Ohm’s Law is an extremely important and handy principle in electronics, thus we must comprehend and memorize its formulae precisely.

• If you want to calculate Voltage ( V ), use the following formula;
• [ V = I x R ]      V (volts) = I (amps) x R (Ω)
• If you want to calculate Current ( I ), use the following formula:
• [ I = V ÷ R ]      I (amps) = V (volts) ÷ R (Ω)
• If you want to calculate Resistance ( R ), use the following formula:
• [ R = V ÷ I ]      R (Ω) = V (volts) ÷ I (amps)

Ohm’s Law Triangle

The “Ohm’s Law Triangle” is a shortcut that we may utilize in place of learning the formulae.

Voltage (V) sits at the top of this triangle, while the lower corners are occupied by Current (I) and Resistance (R).

Every term’s location in the triangle corresponds to where it appears in the real Ohm’s Law formulae.

Thus, examining the triangle could help in remembering of the appropriate formula.

The basic Ohm’s Law equation may be expressed in a number different ways by simply changing around the terms.

These new versions are comparable to distinct tools in our toolbox; one is meant to be used in conjunction with the other two to determine a particular value (voltage, current, or resistance).

We can forecast how current will behave in a circuit using Ohm’s Law.

Consider applying 1 volt (V) to a 1 ohm (Ω) resistor. The law states that this will result in a precise 1 amp (A) of electricity flowing.

Generally speaking, at a given voltage, less current will flow the higher the resistance. “Ohmic” refers to devices that obey Ohm’s Law, which states that current is proportionate to voltage and includes resistors and wires.

Transistors and diodes are examples of devices that defy this law and are referred to be “non-ohmic.”

Understanding Electrical Power in Circuits

We can think of electrical power (P), as the rate at which energy flows in a circuit, which can be either absorbed or produced.

Imagine a voltage source like a battery which injects power into the circuit.

Alternatively, devices connected in the circuit like light bulbs or heaters absorbs this power.

These devices subsequently convert the electrical power into heat, light, or sometimes both.

Generally, the higher their wattage rating they have, the more power they consume.

So how do we measure this power flow?

We use the symbol P and we calculate it by multiplying the voltage (V) by the current (I) flowing in the circuit.

The unit for power is watt (W). Now, different devices use varying amounts of power.

To handle these different scales, we use prefixes with watts.

For example, milliwatts (mW) represent a thousandth of a watt (1 mW = 10^-3 W), and kilowatts (kW) represent a thousand watts (1 kW = 10³ W).

Next, we can use Ohm’s Law (V = I * R) to our advantage.

By substituting the values for voltage, current, and resistance in this formula, we can actually derive the formula for electrical power itself.

• To calculate Power (P), we can use the following formula:
• [ P = V x I ]      P (watts) = V (volts) x I (amps)
• Alternatively, we can also use the following formula:
• [ P = V² ÷ R ]      P (watts) = V² (volts) ÷ R (Ω)
• Here’s yet another formula for calculating power:
• [ P = I² x R ]      P (watts) = I² (amps) x R (Ω)

The Power Triangle

Similar to the Ohm’s Law Triangle, the “Power Triangle” is another useful tool.

We can more easily recall the connections between power, voltage, and current thanks to this triangle.

Power, voltage, and current are positioned in the power triangle in a manner similar to the Ohm’s Law Triangle, to represent their respective positions in the power formulae.

This layout helps us remember the right formula to employ when performing power calculations.

We may experiment with the power formula to obtain several variations, much as we do with Ohm’s Law.

These new versions are similar to various tools in our toolbox; one is meant to be used in conjunction with the other two in order to determine a particular quantity (power, voltage, or current).

To determine the amount of electrical power in a circuit, we can use one of three formulas. These equations tell us if that component is producing or consuming power.

Regardless of the formula we apply, if the power result is positive (+P), it indicates that the component is absorbing power, much like a lightbulb using electricity to shine.

A negative number (-P) for power, on the other hand, indicates that the component is truly producing power, much like a battery that is forcing electricity into the circuit. Batteries and generators are two instances of components which generate electricity.

Power Rating of a Load

Electrical components have a “power rating” expressed in watts (W), much like a vehicle engine. This rating indicates the most quantity of electricity that it can safely handle and transform into other energy forms, such as motion, heat, or light.

A tiny quantity of power may be converted into heat using a resistor rated at 1/4W.
A higher quantity of power can be converted into light (and some heat) by a light bulb with a 100W rating.

Electrical devices function similarly to power converters. They absorb electricity and transform it into another form:

Motors provide mechanical force, like spinning a fan, by using electricity.

In contrast, generators transform mechanical force, like a water wheel, into electrical energy.

Electricity is converted into both light and some heat by light bulbs.

You may occasionally find power ratings expressed in horsepower (hp) rather than watts, particularly for bigger motors. It’s comparable to measuring speed in kilometers or miles per hour. Although they use different units, they both measure the same thing.

This is the rate of conversion:

746 watts (W) is equivalent to one horsepower (hp).
Therefore, the true rating of a 2-horsepower motor is 1.5 kW, or 1492 watts (2 horsepower x 746 W).

Ohm’s Law Pie Chart

Learning a few formulae by heart may be necessary to fully understand Ohm’s Law. However, the “Ohm’s Law Pie Chart” is a useful tool that can assist!

All of the Ohm’s Law formulas, for voltage, current, resistance, and even power, are combined into one handy visual assistance with this pie chart. It functions with circuits that use direct current (DC) or alternating current (AC).

Assume that the pie is divided into slices, each of which stands for a distinct formula.

You may get the missing value by consulting the slice that corresponds to your circumstance, depending on the two numbers (voltage, current, or resistance) you already know.

Without having to memorize the entire formula, this pie chart is an excellent tool for rapidly recalling the right answer!

Table for Ohm’s Law Matrix

Apart from the Ohm’s Law Pie Chart, we can also utilize a useful instrument known as a “Ohm’s Law Matrix.”

For convenience, each of the individual Ohm’s Law equations is listed in this table.

When you know the other two, it assists you in determining the missing value (voltage, current, or resistance), just like a pie chart does. Consider it a handy reference for resolving Ohm’s Law issues!

Solving an Ohm’s Law problem

Calculate the Voltage (V), Current (I), Resistance (R), and Power (P) using the information provided the following diagram:

• Voltage   [ V = I * R ] = 2 x 6Ω = 12V
• Current   [ I = V ÷ R ] = 12 ÷ 6Ω = 2A
• Resistance   [ R = V ÷ I ] = 12 ÷ 2 = 6 Ω
• Power   [ P = V * I ] = 12 x 2 = 24W

Power can only be present in a circuit when there is both voltage and current.

When a circuit is open, voltage is present, but no current flows. The absence of current results in zero power (V * 0 = 0), because power (V * I) is found by multiplying voltage by current.

Conversely, when there is a short circuit, current flows through the circuit, but the voltage decreases to zero (V = 0). Again, because the voltage is zero, the power calculation (V * I) is also zero (0 * I = 0).

Recall that the formula for calculating power in a circuit is voltage (V) times current (I). As a result, the total power used (dissipated) remains constant regardless of whether the circuit contains:

Low current and high voltage
High current and low voltage

What Happens to the Power?

This wasted power can take a variety of forms:

Heat: The conversion of electrical energy into warmth is a typical feature of devices like resistors and heaters.
Mechanical Work: Motors generate movement, such as the whirling of a fan, by using electrical power.
Energy: Batteries store electrical energy for later use, while lights (lamps) transform electricity into light energy.

Understanding Electrical Energy Flow in Circuits

Electrical energy is defined by how much work it can perform, which is measured in joules.

This electrical energy is the product of the usual power (watts) multiplied by the usage duration (seconds).

So, you can determine the total energy consumed in watt-seconds, which is the same as joules, if you know how much power (watts) and how long (seconds) anything is on.

In simple terms, Power = Voltage * Current, and Energy = Power * Time.

Therefore, the energy and all of this electrical power related things are related, and they both require joules!

Assume you have a bucket full of joules (energy). The rate at which you pour energy out of a bucket is equivalent to electrical power.

One watt is produced if one joule of energy is released per second.

Watts therefore indicate the rate at which energy is being utilized rather than the overall quantity.

An alternative way of understanding it is the speed at which energy flows across a circuit.

Electrical Power and Energy Triangle

or if you want to calculate the different individual quantities:

As we previously discussed, the unit of measurement for electrical energy is joules (J), or watts per second. However, when estimating energy usage over time, particularly for appliances, joules may grow very large.

Consider turning on a 100-watt lightbulb for a full day. It would need an astounding 8,640,000 joules (J) of energy!

For the sake of simplicity, larger quantities such as megajoules (MJ) or kilojoules (kJ) are used in these computations. These units are just larger versions of joules, similar to “kilo” or “mega” meters.

An energy consumption of 8.64 megajoules (MJ), in our lightbulb illustration, would be far more reasonable!

Kilowatt-hour (kWh): A unit of electrical energy use

A common method to calculate how much power an appliance requires is to use a kWh.

It takes into account the power of the device, the amount of electricity it consumes at a time, as well as the duration of usage.

Consider it similar to calculating a car’s mileage traveled. You take into account both time (how far it travels) and speed (how quickly it moves).

As an illustration, a 1000-watt appliance using one hour of power consumes one kWh of electricity. This is the same amount of electricity used by a 100-watt lightbulb that is left on for ten hours (since the lightbulb operates longer but with less power).

kWh: The standard unit for electricity bills

The energy meter in your house uses this unit to calculate the overall amount of power you consume.
Your power bill will increase in proportion to your kWh usage, which indicates that you have used more electricity overall.

Real-world example of kWh usage

Consider using a space heater with 1000 watts for an hour. One kWh of power is used for this.

The same amount, one kWh, would be used if two 1000-watt space heaters were used instead, but only for thirty minutes each, or half an hour. (Though in practice the power consumption would just double for a shorter period of time).

Despite the fact that the wattage is doubled, using 1000 watts for an hour uses the same amount of energy as using 2000 watts for 30 minutes. This is thus because total kWh accounts for both time and power.

Consider a 100-watt lightbulb as an example. It would need to run for ten hours in order to utilize one kWh of power.

Since there are 1000 watts in a kilowatt, we can compute this by multiplying the wattage (100 watts) by the duration (10 hours) and dividing the result by 1000.

1 kWh is equal to (100 watts * 10 hours) / 1000 watts/kWh.

References: Ohm’s Law

Ohm’s Law and Ohm’s Power Loss?