Ohm's Law: Identifying the Constant Component

The question asks to identify the constant component in Ohm's Law when voltage is proportional to current in a conductor. Let's break down Ohm's Law and the relationship it describes.

Understanding Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that describes the relationship between voltage ($V$), current ($I$), and resistance ($R$) in a conductor. It states that for a conductor at constant temperature, the electric current passing through it is directly proportional to the voltage difference across its ends.

Mathematically, Ohm's Law can be represented as:

$V \propto I$

This proportionality can be expressed as an equation by introducing a constant of proportionality. This constant is the electrical resistance ($R$) of the conductor.

The formula is:

$V = IR$

In this equation:

• $V$ represents Voltage, measured in Volts (V).
• $I$ represents Current, measured in Amperes (A).
• $R$ represents Resistance, measured in Ohms ($\Omega$).

The law essentially states that voltage is equal to the current multiplied by the resistance. When we say voltage is proportional to current, it means that if you increase the voltage, the current increases proportionally, assuming the resistance remains unchanged.

Analyzing the Options

Let's examine the given options in the context of Ohm's Law:

• Conductance: Conductance ($G$) is the reciprocal of resistance ($G = 1/R$). While related, it's not the constant factor in the standard form $V = IR$. If the relationship were expressed as $I = GV$, then conductance would be the constant. However, the question specifies voltage proportional to current.
• Resistance: As derived from the law $V = IR$, resistance ($R$) is the factor that relates voltage and current. For many conductors under constant conditions (like temperature), resistance is constant, making voltage directly proportional to current. This matches the condition described in the question.
• Inductance: Inductance ($L$) is a property of electrical conductors that relates to the magnetic field created by electric current. It is measured in Henrys (H) and is associated with inductors, not the basic resistive property described by Ohm's Law for voltage and current proportionality.
• Capacitance: Capacitance ($C$) is the ability of a system to store an electric charge. It is measured in Farads (F) and is associated with capacitors. It does not represent the constant factor in the basic Ohm's Law relationship between voltage and current in a resistor.

Conclusion

Based on Ohm's Law, $V = IR$, when voltage ($V$) is directly proportional to current ($I$), the factor of proportionality, which is Resistance ($R$), must remain constant. Therefore, resistance is the constant component under the conditions stated.