Ohm's Law

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.

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.