Ohm's Law

Ohm's Law, discovered by the German scientist George Simon Ohm, describes the relationship between the current (I) flowing through a conductor and the potential difference (V) applied across its ends. According to this law, the current flowing through a conductor is directly proportional to the potential difference across its ends, provided the temperature and other physical conditions remain constant.

If the physical state of a conductor remains constant, the current (I) flowing through it is directly proportional to the potential difference (V) between its two ends.

I ∝ V

I = kV  (k = constant of proportionality)

I×`"1"/"K"`=V ( `"1"/"K"`= R = Resistance of the conductor )

I × R = V Hence, V = I × R or R = `"V"/"I"`

This is known as Ohm’s law.

V = I × R (Volts = amps times ohms)

`I = V/R` (Amps = volts divided by ohms)

`R = V/I` (Ohms = volts divided by amps)

The length, area of cross-section, temperature, and material composition of a conductor define its physical state. We can obtain the SI unit of resistance from the above formula. Potential difference and current are measured in volts and amperes, respectively. The unit of resistance is called an ohm. It is indicated by the symbol Ω.

`"1 Volt"/"1 Ampere"`= 1 Ohm (W)

Resistance of one ohm: If one ampere of current flows through a conductor when one-volt potential difference is applied between its ends, then the resistance of the conductor is one ohm.

Limitations:

• Ohm’s Law does not apply to unilateral circuits (e.g., circuits with diodes or transistors) that allow current flow only in one direction.
• It fails in non-linear elements, where current is not proportional to voltage, such as semiconductors, electrolytes, and superconductors.
• Resistance is not always constant; in components like thermistors and filament bulbs, resistance changes with temperature, making Ohm’s Law invalid.
• It is not applicable to high-frequency AC circuits where inductance and capacitance affect the relationship between voltage and current.

Applications:

• It is used to calculate current, voltage, and resistance in electrical circuits.
• Helps determine power consumption using the formula P = VI.
• Used in circuit design to ensure proper voltage and current distribution.
• Helps in analysing resistivity, drift velocity, and electrical properties of materials.
• Essential in electrical safety calculations, such as determining fuse ratings and wire thickness for preventing overheating.
• Used in industries for troubleshooting electrical appliances and checking circuit functionality.

The reciprocal of resistance is called conductllnce. It is denoted by the letter G. 

Statement: Ohm’s Law

"The electric current flowing through a conductor is directly proportional to the potential difference across its ends, provided the temperature and other physical conditions of the conductor remain constant."

Mathematically,

I ∝ V or V = I R

where:

• V = Potential difference (in volts)
• I = Current (in amperes)
• R = Resistance of the conductor (in ohms, Ω)

Explanation:

When two conductors at different electric potentials are joined by a metallic wire, electrons flow from the conductor at a lower potential (excess electrons) to the one at a higher potential (deficit of electrons). This movement of electrons results in an electric current.

• The current continues to flow until both conductors reach the same potential.
• For continuous current flow, a constant potential difference must be maintained across the ends of the conductor (e.g., using a battery or power supply).

Derivation / Mathematical Proof:

From Ohm’s Law:

I ∝ V ⇒ \[\frac {V}{I}\] = constant

This constant is defined as the resistance (R) of the conductor. Therefore,

V = I R   ---(1)

This is the mathematical form of Ohm’s Law.

Special Case:

If the current I = 1 A, then:

V = R

This implies that the resistance of a conductor is numerically equal to the potential difference across it when 1 ampere of current flows through it.

Conclusion:

Ohm's Law provides a fundamental relationship between voltage, current, and resistance in an electric circuit. It is widely used in the design and analysis of electrical and electronic systems.