Ohm’s law proportionality check: If resistance remains constant in a circuit, how are current (I) and voltage (V) related?

Introduction / Context:
Ohm’s law is the cornerstone of DC and low-frequency AC circuit analysis. Understanding proportionality with a fixed resistance explains how sensors, voltage dividers, and loads behave as supply voltage varies. This question reinforces the linear relationship between voltage and current when resistance does not change.

Given Data / Assumptions:

• Resistance R is constant (temperature and nonlinearity ignored).
• Simple two-terminal resistive element.
• Quasi-static conditions where reactive effects are negligible.

Concept / Approach:

Ohm’s law states V = I * R. With R fixed, I = V / R, so I is directly proportional to V. Doubling V doubles I; halving V halves I. This is the basis of linear resistor behavior and enables predictable control of current by setting voltage or resistance.

Step-by-Step Solution:

Verification / Alternative check:

Measure current at two voltages keeping the same resistor. The ratio I2/I1 equals V2/V1. This linearity is observed in standard resistors within rated power and temperature ranges.

Why Other Options Are Wrong:

• Inversely proportional: would require I ∝ 1/V, which contradicts Ohm’s law for fixed R.
• “The same” or “unable to produce energy”: not a relationship statement and not relevant.
• “Unrelated unless frequency is specified”: frequency matters for reactive elements, not ideal resistors.

Common Pitfalls:

• Confusing constant-resistance behavior with constant-current sources (where current is fixed and voltage varies).
• Ignoring temperature coefficients that can slightly change R in real components.

Final Answer:

directly proportional