Understanding the Relationship Between Potential Difference and Current

The question asks what happens to the current flowing through a conductor when the potential difference across its ends is halved. To answer this, we need to understand the fundamental relationship between potential difference (voltage), current, and resistance in an electrical circuit. This relationship is described by Ohm's Law.

Applying Ohm's Law

Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them, provided the temperature and other physical conditions remain constant. Mathematically, Ohm's Law is expressed as:

\(V = IR\)

Where:

• \(V\) is the potential difference (voltage) across the conductor.
• \(I\) is the current flowing through the conductor.
• \(R\) is the resistance of the conductor.

From this equation, we can express the current \(I\) as:

\(I = \frac{V}{R}\)

Analyzing the Change in Potential Difference

Let's consider the initial condition and the changed condition.

Initial Condition:

• Initial potential difference = \(V_1\)
• Initial current = \(I_1\)
• Resistance of the conductor = \(R\)

According to Ohm's Law:

\(I_1 = \frac{V_1}{R}\) (Equation 1)

Changed Condition:

• The potential difference is halved. New potential difference \(V_2 = \frac{V_1}{2}\)
• Let the new current be \(I_2\)
• The resistance \(R\) of the conductor remains constant (assuming constant temperature and material)

According to Ohm's Law for the changed condition:

\(I_2 = \frac{V_2}{R}\)

Calculating the New Current

Now, substitute the new potential difference \(V_2 = \frac{V_1}{2}\) into the equation for \(I_2\):

\(I_2 = \frac{\frac{V_1}{2}}{R}\)

This can be rewritten as:

\(I_2 = \frac{1}{2} \times \frac{V_1}{R}\)

From Equation 1, we know that \(I_1 = \frac{V_1}{R}\). Substitute \(I_1\) into the equation for \(I_2\):

\(I_2 = \frac{1}{2} \times I_1\)

or

\(I_2 = \frac{I_1}{2}\)

This result shows that the new current \(I_2\) is half of the initial current \(I_1\).

Conclusion based on Potential Difference Change

Therefore, if the potential difference across the ends of a conductor is halved, the current flowing through it also gets halved, assuming the resistance remains constant. This demonstrates the direct proportionality between potential difference and current in a conductor following Ohm's Law.

Revision Table: Key Concepts

Additional Information: Factors Affecting Resistance

While we assumed resistance \(R\) is constant in the Ohm's Law calculation above, it's important to know that the resistance of a conductor depends on several factors:

• Material: Different materials have different inherent resistances (resistivity).
• Length: Resistance is directly proportional to the length of the conductor. Longer conductors have higher resistance.
• Area of Cross-section: Resistance is inversely proportional to the area of the cross-section. Thicker wires have lower resistance.
• Temperature: For most metallic conductors, resistance increases with increasing temperature.

Ohm's Law is strictly applicable to Ohmic conductors where the resistance remains constant over a wide range of voltages and currents. Diodes, transistors, and some other components are non-ohmic.