Ohms Law and Power

The relationship between Voltage, Current, and Resistance in any DC electrical circuit was first discovered by the German physicist Georg Ohm.

Georg Simon Ohm observed that, under consistent temperature conditions, the electric current passing through a set linear resistance is directly linked to the applied voltage and inversely related to the resistance. This interconnection among Voltage, Current, and Resistance constitutes the fundamental concept of Ohms Law, as depicted below.

Ohms Law Relationship

\boxed{\mathbf{Current,(I) = \frac{Voltage,(V)}{Resistance,(R)} , in\,Amperes,(A)}}

By having knowledge of any two values among Voltage, Current, or Resistance, Ohms Law can be applied to determine the third missing value. Ohm’s Law plays a crucial role in various electronic formulas and calculations, underscoring the significance of understanding and accurately recalling these formulas.

To find the Voltage, ( V )

[ V = I x R ]      V (volts) = I (amps) x R (Î©)

To find the Current, ( I )

[ I = V Ã· R ]      I (amps) = V (volts) Ã· R (Î©)

To find the Resistance, ( R )

[ R = V Ã· I ]      R (Î©) = V (volts) Ã· I (amps)

Sometimes, it’s more convenient to recall the relationship defined by Ohm’s Law using visual aids. In this context, the three variables V (Voltage), I (Current), and R (Resistance) are arranged in a triangle, affectionately known as the Ohm’s Law Triangle. The triangle is configured with voltage at the top and current and resistance positioned below, accurately representing the actual arrangement of these quantities within the Ohm’s Law formulas.

Ohms Law Triangle

Rearranging the standard Ohm’s Law equation provides us with various equivalent forms of the same equation:

Applying Ohm’s Law reveals that when a voltage of 1V is applied to a resistor with a resistance of 1Î©, a current of 1A will flow. Additionally, as the resistance value increases, the current flowing for a given applied voltage decreases. Any electrical device or component that adheres to “Ohm’s Law”â€”meaning the current is proportional to the voltage across it (I Î± V)â€”such as resistors or cables, is termed “Ohmic” in nature. On the other hand, devices that do not follow Ohms Law, such as transistors or diodes, are labeled as “Non-ohmic” devices.

Electrical Power in Circuits

Electrical power (P) in a circuit represents the rate at which energy is either absorbed or generated within the circuit. A source of energy, like a voltage, contributes or delivers power, while the connected load consumes it. Devices such as light bulbs and heaters absorb electrical power and transform it into either heat, light, or a combination of both. The higher their wattage rating, the more electrical power they are likely to consume.

The symbol for power is P, calculated as the product of voltage multiplied by the current, with the unit of measurement being the Watt (W). Different prefixes are utilized to denote multiples or sub-multiples of a watt, such as milliwatts (mW = 10^-3W) or kilowatts (kW = 10^3W).

By employing Ohm’s Law and substituting the values of V, I, and R, the formula for electrical power can be derived as follows:

To find the Power (P)

[ P = V x I ]      P (watts) = V (volts) x I (amps)

Also:

[ P = V2 Ã· R ]      P (watts) = V2 (volts) Ã· R (Î©)

Also:

[ P = I2 x R ]      P (watts) = I2 (amps) x R (Î©)

Once more, the three quantities have been arranged within a triangle, referred to as a Power Triangle this time, where power is positioned at the top and current and voltage are located at the bottom. This configuration accurately reflects the actual position of each quantity within the power formulas derived from Ohms Law.

The Power Triangle

Similarly, rearranging the fundamental Ohm’s Law equation for power provides us with various equivalent forms of the same equation, allowing us to determine the various individual quantities:

We observe that there are three potential formulas for computing electrical power in a circuit. If the calculated power is positive (+P) for any formula, it indicates that the component is absorbing power, meaning it is consuming or utilizing power. Conversely, if the calculated power is negative (â€“P), the component is producing or generating power. In other words, it acts as a source of electrical power, as seen in batteries and generators.

Electrical Power Rating

Electrical components are assigned a “power rating” measured in watts, indicating the maximum rate at which the component transforms electrical power into other forms of energy like heat, light, or motion. Examples include a 1/4W resistor or a 100W light bulb.

Electrical devices have the ability to convert one form of power into another. For instance, an electric motor transforms electrical energy into mechanical force, while an electrical generator changes mechanical force into electrical energy. A light bulb converts electrical energy into both light and heat.

While the standard unit of power is the watt (W), certain electrical devices, such as electric motors, are rated in the traditional unit of “Horsepower” (hp). The relationship between horsepower and watts is defined as 1hp = 746W. For example, a two-horsepower motor has a rating of 1492W (2 x 746) or 1.5kW.

Ohms Law Pie Chart

To enhance our comprehension of the relationship between various values, we can consolidate all the Ohm’s Law equations mentioned earlier for determining Voltage, Current, Resistance, and Power into a straightforward Ohms Law pie chart. This chart proves useful in both AC and DC circuits and facilitates calculations.

In addition to utilizing the Ohm’s Law Pie Chart illustrated above, we can organize the individual Ohm’s Law equations into a straightforward matrix table, as presented below. This provides a convenient reference for calculating unknown values.

Ohms Law Example-1

For the circuit shown below find the Voltage (V), the Current (I), the Resistance (R), and the Power (P).

Voltage   [ V = I x R ] = 2 x 12Î© = 24V

Current   [ I = V Ã· R ] = 24 Ã· 12Î© = 2A

Resistance   [ R = V Ã· I ] = 24 Ã· 2 = 12 Î©

Power   [ P = V x I ] = 24 x 2 = 48W

Power within an electrical circuit manifests only when both voltage and current are concurrently present. In scenarios like an open-circuit condition, where voltage exists but no current flows (I = 0), the power dissipated within the circuit is also 0, given that V * 0 equals 0. Similarly, in a short-circuit condition, where current flows but there is no voltage (V = 0), the power dissipated within the circuit remains 0, as 0 * I equals 0.

The electrical power, being the product of V (voltage) and I (current), remains consistent whether the circuit features high voltage and low current or low voltage and high current flow. Generally, electrical power is dissipated in various forms such as heat (in heaters), mechanical work (as in motors), energy in the form of radiation (in lamps), or stored energy (in batteries).

Electrical Energy in Circuits

Electrical energy represents the capability to perform work, and the unit of work or energy is the joule (J). The electrical energy consumed is the result of multiplying power by the duration it was utilized. Hence, if we know the power in watts being consumed and the time in seconds for which it is used, we can determine the total energy used in watt-seconds. In simpler terms, the relationship is expressed as Energy = power x time, and since Power = voltage x current, electrical power is inherently linked to energy. The unit designated for electrical energy is the watt-seconds or joules.

\boxed{\mathbf{Electrical\,Energy = Power\,(P) \times Time\,(T)) )}}

Electrical power can be alternatively described as the rate at which energy is transferred. If one joule of work is either absorbed or delivered consistently over one second, the corresponding power will be equivalent to one watt. In other words, power can be defined as “1 Joule per second = 1 Watt.” This implies that one watt is equal to one joule per second, emphasizing that electrical power is essentially the rate of performing work or transferring energy.

Electrical Power and Energy Triangle

or to find the various individual quantities:

Previously, we mentioned that electrical energy is defined as watts per second or joules. Although electrical energy is measured in joules, it can result in very large values when calculating the energy consumed by a component.

For instance, if a 100-watt light bulb is left “ON” for 24 hours, the energy consumed will be 8,640,000 joules (100W x 86,400 seconds). To simplify the expression of such large numbers, prefixes such as kilojoules (kJ = 10^3J) or megajoules (MJ = 10^6J) are often used. In this example, the energy consumed would be 8.64MJ (mega-joules).

Dealing with joules, kilojoules, or megajoules for expressing electrical energy can involve complex calculations with large numbers and multiple zeros. To make it more manageable, electrical energy consumed is often expressed in kilowatt-hours (kWh).

If the electrical power consumed (or generated) is measured in watts or kilowatts (thousands of watts), and the time is measured in hours rather than seconds, the unit of electrical energy becomes kilowatt-hours (kWh). Using this unit, the 100-watt light bulb example would consume 2,400 watt-hours or 2.4 kWhr, which is a more practical representation than the 8,640,000 joules.

One kilowatt-hour (1 kWhr) represents the amount of electricity used by a device rated at 1000 watts in one hour and is commonly referred to as a “Unit of Electricity.” This is what is measured by the utility meter, and it is what consumers purchase from electricity suppliers when receiving bills.

Kilowatt-hours are the standard units of energy used by electricity meters in homes to calculate the amount of electrical energy consumed, determining the cost. For example, if you switch on an electric fire with a heating element rated at 1000 watts and leave it on for 1 hour, you will have consumed 1 kWh of electricity. Switching on two electric fires, each with 1000-watt elements, for half an hour would result in the same total consumption of electricityâ€”1 kWh.Therefore, consuming 1000 watts for one hour uses the same amount of power as 2000 watts (twice as much) for half an hour (half the time).

Now that we understand the relationship between voltage, current, and resistance in a circuit, in the next tutorial related to DC circuits, we will explore the standard electrical units used in electrical and electronic engineering to calculate these values. We will see that each value can be represented by either multiples or sub-multiples of the standard unit.

Hello friends, my name is Trupal Bhavsar, I am the Writer and Founder of this blog. I am Electronics Engineer(2014 pass out), Currently working as Junior Telecom Officer(B.S.N.L.) also I do Project Development, PCB designing and Teaching of Electronics Subjects.

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