# Ohm’s Law

Whenever the fan in your room is on and when you feel cold you reduce the fan’s speed. For doing so you use the speed control knob on the switchboard. But how does the knob work? What’s its mechanism? The knob works on the principles of ‘Ohm’s Law’. But what does Ohm’s law of current electricity state? Let us study Ohm’s law of current electricity.

## Ohm’s Law of Current Electricity

Ohm’s Law of Current Electricity is named after the scientist ”Ohm”. Most basic components of current electricity are voltage, current, and resistance. Ohm’s law shows a simple relation between these three quantities.

Ohm’s law of current electricity states that the current flowing in a conductor is directly proportional to the potential difference across its ends provided the physical conditions and temperature of the conductor remains constant.

Voltage= Current× Resistance
V= I×R

where V= voltage, I= current and  R= resistance. The SI unit of resistance is ohms and is denoted by Ω. In order to establish the current-voltage relationship, the ratio V / I remains constant for a given resistance, therefore a graph between the potential difference(V) and the current (I) must be a straight line.

This law helps us in determining either voltage, current or impedance or resistance of a linear electric circuit when the other two quantities are known to us. It also makes power calculation simpler.

### Limitations of Ohm’s Law of Current Electricity

• The law is not applicable to unilateral networks. Unilateral networks allow the current to flow in one direction. Such types of network consist of elements like a diode, transistor, etc.
• Ohm’s law is also not applicable to non – linear elements. Non-linear elements are those which do not have current exactly proportional to the applied voltage that means the resistance value of those elements changes for different values of voltage and current. Examples of non – linear elements are the thyristor.
• The relation between V and I depends on the sign of V. In other words, if I is the current for a certain V, then reversing the direction of V keeping its magnitude fixed, does not produce a current of the same magnitude as I in the opposite direction. This happens for example in the case of a diode.

### How do we find the unknown Values of Resistance?

It is the constant ratio that gives the unknown values of resistance. For a wire of uniform cross-section, the resistance depends on the length l and the area of cross-section A. It also depends on the temperature of the conductor. At a given temperature the resistance,

R = $$\frac{ρ l}{A}$$

where ρ is the specific resistance or resistivity and is characteristic of the material of wire. Using the last equation,

V = I × R = $$\frac{I ρ l}{A}$$

I/A is called the current density and is denoted by j. The SI unit of current density is A/m². So,

E I = j ρ I

This can be written as E = j ρ or j = σ E, where σ is 1/ρ is conductivity.

## Solved Questions for You

Q1. The unit for electric conductivity is

1. per ohm per cm
2. ohm × cm
3. ohm per second
4. who

Solution: A. We know that R = $$\frac{I ρ l}{A}$$. R has dimensions of an ohm, L has dimensions of length A has dimensions of (length)². Therefore, ρ has dimensions of ohm-cm.

Q2. What will happen to the current passing through a resistance, if the potential difference across it is doubled and the resistance is halved?

1. Remains unchanged
2. Becomes double
3. Becomes half
4. It becomes four times.

Solution: A. Using ohm’s law

I = $$\frac{V}{R}$$

I’ = $$\frac{2V}{R/2}$$

so, I’ = 4I

Hence the current becomes four times.

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