Ohm's Law

In 1828, George Simon Ohm, a German physicist, derived a relationship between electric current and potential difference. This relationship is known as Ohm’s law. Certain formulas in Physics are so prevalent that they become popular knowledge that you end up memorising without trying. In the field of Modern Physics, it is E=m⋅c2. Similarly, in the field of current electricity, it is the Ohm’s law about which we will be studying in this article.


What is Ohm’s Law?

Ohm’s Law states that the current flowing through a conductor is directly proportional to the potential difference applied across its ends, provided the temperature and other physical conditions remain unchanged. Mathematically it can be represented as,

Potential difference ∝ Current
V I

( When the value of V increases the value of I increases simultaneously)

V = IR

Where,

  • V is Voltage in volts (V)
  • R is Resistance in ohm (Ω)
  • I is Current in Ampere (A)

Ohm’s Law Formula

As an equation, the Ohm’s Law serves as an algebraic recipe for calculating the current when the resistance and the potential difference are known. Likewise, if any two parameters in the equation are known, then the unknown third parameter can be easily calculated as follows:

  • To find Voltage(V),
V = IR
  • To find Current(I),
\(I=\frac{V}{R}\)
  • To find Resistance(R),
\(R=\frac{V}{I}\)

Ohm’s Law Application

The main applications of Ohm’s law are:

  1. To determine the voltage, resistance or current of an electric circuit.
  2. Ohm’s law is used to maintain the desired voltage drop across the electronic components.
  3. Ohm’s law is also used in dc ammeter and other dc shunts to divert the current.

Ohm’s Law Limitation

Following are the limitations of Ohm’s law:

  1. Ohm’s law is not applicable for unilateral electrical elements like diodes and transistors as they allow the current to flow through in one direction only.
  2. For non-linear electrical elements with parameters like capacitance, resistance etc the voltage and current won’t be constant with respect to time making it difficult to use Ohm’s law.

Derivation of Ohm’s Law

vd = \((\frac{-eE\tau}{m})\) (Eq. 1)

E = \((\frac{-V}{L})\) (Eq. 2)

From Eq. 1 and Eq. 2;

\(v_{d}=\frac{(eV\tau )}{mL}\)

V = \(\frac{(v_{d}mL)}{e\tau }\)

Also I = Anevd

\(v_{d}=\frac{I}{Ane}\) (Eq. 3)

Using Eq. 3

\(V=\frac{ImL}{Anee\tau }\)

\((\frac{(mL)}{Ane^{2}\tau }I)\)

\((\frac{\rho L}{A})I\)

Where ρ = \((\frac{m}{ne^{2}\tau })\)

Therefore, V = RI

Ohm’s Law Magic Triangle

Ohm's Law

As discussed, the Ohm’s law is defined by the equation V = IR. Ohm’s Law Triangle is helpful in remembering the Ohm’s law equation while solving problems. Here, the three quantities V, I and R are superimposed into a triangle with the voltage at the top and current and resistance below. The magic V I R  triangle can be used to calculate all formulations of Ohm’s law.

The triangle for Ohm’s law:

Ohm’s Law Magic Triangle

  • If the value of voltage is asked and the values of the current and resistance are given, then to calculate voltage simply cover V at the top. So, we are left with the I and R orI X R. So, the equation for Voltage is Current multiplied by Resistance. An example of how the magic triangle is employed to determine the voltage using Ohm’s law is given below.

Ohm’s Law Magic Triangle
Example 1: If the resistance of an electric iron is 50Ω and 3.2A Current flows through the resistance. Find the voltage between two points.

Ans. Given, Resistance (R) = 50Ω
Current (I) = 3.2A
Therefore,
Voltage (V) = I X R = 3.2A x 50 Ω =160V

  • If the value of Resistance is asked and the values of the current and voltage are given, then to calculate resistance simply cover the R, we are left with the V at the top and I to the bottom left or V ÷ I.

Ohm’s Law Magic Triangle
Example 2: An EMF source of 8.0 V is connected to a purely resistive electrical appliance (a light bulb). An electric current of 2.0 A flows through it. Consider the conducting wires to be resistance free. Calculate the resistance offered by the electrical appliance.

Ans. Given,
Voltage (V) = 8.0 V
Current (I) = 2.0 A

Therefore,
Resistance (R) = V ÷ I = \(\frac{V}{I}\)

= \(\frac{8}{2} = 4\)

  • If the value of current is asked and the values of the resistance and voltage are given, then to calculate current simply cover the I. We are left with Voltage over Resistance or V ÷ R. So the equation for Current is Voltage divided by Resistance.

Ohm’s Law Magic Triangle
Example 3: If the filament resistance of an electric bulb is 330 Ω and Potential difference of two points 110V. Find the current flowing through the filament.

Ans. Given,
Resistance (R) = 330 Ω
Voltage (V) = 110V

Therefore,
Current (I) = V ÷ R
I = \(\frac{V}{R}\)

= \(\frac{110}{330} = 0.3A\)

Calculation of Electrical Power

The rate at which energy is converted from the electrical energy of the moving charges to some other form of energy like mechanical energy, heat, magnetic fields or energy stored in electric fields, is known as electric power. The unit of power is watt. The electrical power can be calculated using the Ohm’s law and by substituting the values of voltage, current and resistance.

Formulae to find power:

  • When the values for voltage and current are given,

P = V x I

  • When the values for voltage and resistance are given,

P = \(V^{2}\div R\)

  • When the values for voltage and current are given,

P = \(I^{2}\times R\)

Power Triangle:

In the power triangle, the power (P) will be on the top and current(I) and voltage (V) at the bottom.

  • When the values of current and voltage will be given, the formula for finding power will be,
P = I x V

Power Triangle

  • When the values of power and voltage will be given, the formula for finding current will be,
I = \(\frac{P}{V}\)

Power Triangle

  • When the values of power and current will be given, the formula for finding voltage will be,
V = \(\frac{P}{I}\)

Power Triangle

Ohm’s Law Pie Chart

Ohms Law Pie Chart

Ohm’s Law Matrix Table

Ohms Law Table

Frequently Asked Questions

What is Ohm’s law simplified?

Ohm’s law states that the current passing through a conductor is proportional to the voltage over the resistance..

How do you calculate current draw?

To calculate the current drawn, divide the power by the operating voltage.

Do all metals obey Ohm’s law?

When the temperature of a metal increases, resistance decreases. Good conductors possess non-zero electrical resistances.

Why is Ohm’s law important?

Ohm’s law formula is used to calculate electrical values so that we can design circuits and use electricity in a useful manner.

1 Comment

  1. Nice app to a students

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