Ohm's Law

Ohm's Law is a fundamental law of current electricity that relates potential difference, current, and resistance in a conductor. It states that for a metallic conductor under constant physical conditions, the current through it is directly proportional to the potential difference across its ends.

Ohm's Law was established by Georg Simon Ohm through experiments on conductors. The law is based on three core quantities:

• Potential Difference (V): Work done per unit charge. 
• Current (I): Rate of flow of electric charge. 
• Resistance (R): Opposition offered to the current. 

Key Idea

• If the conductor and its temperature remain unchanged, increasing the voltage increases the current in the same ratio.

Analogy

• Voltage is like water pressure.
• Current is like water flow.
• Resistance is like a narrow pipe opposing flow.

At constant temperature and other physical conditions, the current flowing through a conductor is directly proportional to the potential difference across its ends.

V ∝ I

V = IR

Other useful forms: I = \[\frac {V}{R}\] or R = \[\frac {V}{I}\]

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.

• 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.

Aim

To verify that the current through a conductor is directly proportional to the potential difference across it at constant temperature.

Apparatus Required

• A nichrome wire (or resistor) of known resistance
• An ammeter (to measure current) — connected in series
• A voltmeter (to measure potential difference) — connected in parallel across the resistor
• A rheostat (variable resistance) — to vary the current
• A battery or cells
• A plug key (switch)
• Connecting wires

Circuit Setup

• The ammeter is placed in series so the same current passes through it.
• The voltmeter is placed in parallel, so it measures the exact potential difference across the resistor only.
• The rheostat is adjusted to change the current through the circuit step by step.

Procedure

1. Set up the circuit as described above.
2. Close the key to allow current to flow.
3. Adjust the rheostat to a low current value.
4. Note the ammeter reading (I) and the corresponding voltmeter reading (V).
5. Increase the current step by step using the rheostat.
6. Record 4–6 sets of V and I values in a table.
7. For each set, calculate the ratio V/I.

Observation Table

Result: The ratio V/I remains nearly constant for all readings, which equals the resistance RR of the conductor.

Graph

• Plot V on the y-axis and I on the x-axis.
• The graph is a straight line passing through the origin.
• This straight-line nature confirms that V ∝ I, which is Ohm's Law.
• The slope of the line gives the resistance R:
  Slope = \[\frac {V}{I}\] = R

A steeper slope means higher resistance; a gentler slope means lower resistance.

Conclusion

Since V/I = constant and the V-I graph is a straight line through the origin, the experiment confirms that:

The conductor obeys Ohm's Law under constant temperature conditions.

Precautions

• Do not leave the circuit closed for long — the wire heats up, changing resistance and invalidating results.
• Use the rheostat carefully to avoid sudden, large currents.
• Ensure the ammeter has low resistance and the voltmeter has high resistance for accurate readings.

A current of 0.5 A flows through a resistor when 1.5 V is applied. Find resistance.

Answer: 6 Ω

• What we know: The voltage (V) is 12 V and the resistance (R) is 24.
• The formula: Ohm's Law states that current (I) equals voltage divided by resistance: \[I = \frac{V}{R}\]
• The calculation: Plugging in the given numbers gives: \[I = \frac{12}{24} = 0.5\text{ A}\]

The current flowing through the resistor is 0.5 A (Amperes).

• Electric appliances are designed using current-voltage-resistance relations.
• Electricians use Ohm's Law while checking wiring and circuit safety.
• Resistors in mobile chargers, LEDs, and electronic boards are selected using this law.