Ohm's Law is a fundamental principle in electricity that describes the relationship between potential difference, current, and resistance in an electrical circuit. It states that the potential difference (voltage) across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature remain constant.

Understanding Ohm's Law and V=IR

The mathematical representation of Ohm's Law is given by:

Where:

• V represents the potential difference (voltage) across the conductor, measured in Volts (V).
• I represents the current flowing through the conductor, measured in Amperes (A).
• R represents the resistance of the conductor, measured in Ohms (\(\Omega\)).

This formula can be rearranged to solve for resistance:

Analyzing Conditions: Constant Potential Difference and Increasing Current

The question provides specific conditions:

• The potential difference (V) remains constant.
• The current (I) increases.

We need to determine how the resistance (R) changes under these conditions based on Ohm's Law.

Determining Resistance Change Based on Ohm's Law

Using the rearranged formula for resistance, \(R = \frac{V}{I}\), we can analyze the relationship when V is constant and I increases.

Let's consider the relationship between R, V, and I:

• If V is constant, Resistance (R) is inversely proportional to Current (I). This means if Current goes up, Resistance must go down, and vice-versa, assuming V is held steady. Mathematically, this can be written as \(R \propto \frac{1}{I}\) when V is constant.

Given that the potential difference (V) is held constant and the current (I) is increasing, the value of the ratio \(\frac{V}{I}\) will decrease because the numerator (V) is fixed and the denominator (I) is getting larger.

Since \(R = \frac{V}{I}\), a decrease in the value of \(\frac{V}{I}\) directly means a decrease in the resistance (R).

Let's look at the options based on our analysis:

• Resistance unchanged: This is incorrect because with V constant and I increasing, R must change.
• Resistance increases: This is incorrect because R and I are inversely proportional when V is constant.
• Potential difference decreases: This contradicts the given condition that potential difference remains constant.
• Resistance decreases: This matches our conclusion based on the inverse relationship between R and I when V is constant.

Therefore, if the current (I) increases while the potential difference (V) remains constant, the resistance (R) must decrease according to Ohm's Law.

Revision Table: Key Ohm's Law Concepts

Additional Information: Factors Affecting Electrical Resistance

While Ohm's Law describes the relationship between V, I, and R for a given resistor under constant physical conditions, the resistance of a conductor itself depends on several factors:

• Material: Different materials have different inherent resistances. Conductors like copper and aluminum have low resistance, while insulators like rubber and glass have very high resistance.
• Length (L): Resistance is directly proportional to the length of the conductor. A longer wire has more resistance (\(R \propto L\)).
• Cross-sectional Area (A): Resistance is inversely proportional to the cross-sectional area of the conductor. A thicker wire has less resistance (\(R \propto \frac{1}{A}\)).
• Temperature: For most conductors, resistance increases with increasing temperature. For some materials like semiconductors, resistance may decrease with temperature.

The formula relating these factors is \(R = \rho \frac{L}{A}\), where \(\rho\) (rho) is the resistivity of the material.