Ohm’s law behavior in a purely resistive circuit: If the applied voltage increases while resistance is constant, does the current increase as well?

Introduction / Context:
Ohm’s law is foundational for DC and low-frequency AC analysis in resistive circuits. This question checks proportional relationships among voltage, current, and resistance.

Given Data / Assumptions:

• Purely resistive element with constant resistance R (no reactive components).
• Voltage V is varied; R is held constant.
• Temperature changes are negligible so R does not drift.

Concept / Approach:
Ohm’s law states V = I * R. For a fixed R, current I = V / R, so I is directly proportional to V. Doubling V doubles I, and halving V halves I. This proportionality holds for both DC and AC at frequencies where the resistor’s behavior is ideal.

Step-by-Step Solution:

Verification / Alternative check:
Power relation P = V * I = V^2 / R shows power grows with the square of voltage at fixed R, consistent with I rising linearly with V.

Why Other Options Are Wrong:

• Current unchanged (option b) contradicts I = V / R.
• Current decreases (option c) reverses the dependence.
• “Depends on power factor” (option d) is irrelevant in a purely resistive load where power factor is 1.

Common Pitfalls:
Ignoring that real resistors heat and change resistance slightly; within normal ranges, the ideal model is accurate for analysis.

Final Answer:
Yes — current increases with voltage when R is constant.