The question asks us to identify the physical quantity that is directly proportional to the current flowing through a resistor, assuming the temperature stays constant. This relationship is a fundamental concept in electricity, described by Ohm's Law.

Understanding Ohm's Law and Resistors

Ohm's Law describes the relationship between voltage (potential difference), current, and resistance in an electrical circuit. It states that the electric current through a metallic conductor is directly proportional to the voltage across its ends, provided the temperature and other physical conditions remain unchanged.

In simpler terms, if you increase the voltage across a resistor, the current through it will increase proportionally, as long as the resistor's temperature doesn't change significantly.

Analyzing the Options

Let's look at the given options:

• Potential difference: This is the voltage across the ends of the resistor. Ohm's Law directly relates potential difference and current.
• Resistivity: This is an intrinsic property of the material the resistor is made of. It describes how strongly the material resists the flow of electric current. Resistivity is constant for a given material at a specific temperature and does not change with the current or potential difference across the resistor.
• Charge: This refers to the fundamental property of matter that experiences a force when placed in an electromagnetic field. While current is the rate of flow of charge, Ohm's Law describes the relationship between potential difference and the rate of charge flow (current), not charge itself.
• Resistance: This is the property of a resistor that opposes the flow of electric current. For an ohmic resistor (one that obeys Ohm's Law), resistance is constant under constant temperature and does not depend on the potential difference or current.

Applying Ohm's Law to the Question

The statement in the question is a direct rephrasing of Ohm's Law:

"The ______ across the ends of a resistor is directly proportional to the current through it, provided its temperature remains the same."

According to Ohm's Law, the potential difference (V) across a resistor is directly proportional to the current (I) flowing through it, provided the resistance (R) and temperature are constant. Mathematically, this is expressed as:

\[V \propto I\] or \[V = IR\]

Here:

• \(V\) is the potential difference across the resistor.
• \(I\) is the current flowing through the resistor.
• \(R\) is the resistance of the resistor (constant at a constant temperature).

Therefore, the quantity that is directly proportional to the current through the resistor, under constant temperature, is the potential difference across its ends.

Conclusion on Potential Difference and Current

Based on Ohm's Law, the potential difference across the ends of a resistor is directly proportional to the current flowing through it when the temperature is kept constant. This fits perfectly with the description provided in the question.

Revision Table: Key Electrical Concepts

Additional Information on Electrical Properties

While potential difference is directly proportional to current according to Ohm's Law, it's important to understand the other terms too. Resistivity is a material property, meaning it depends only on what the material is and its temperature, not its shape or the voltage/current applied. Resistance, on the other hand, depends on the material's resistivity, its length, and its cross-sectional area. For many materials, resistance stays constant at a constant temperature, making the potential difference-current proportionality valid.