Direct Ohm’s law implication — for a fixed-value resistor, if the voltage applied across it increases, how does the current through it change (assuming temperature effects are negligible)?

Introduction / Context:
Ohm’s law gives an immediate relationship between the voltage across a resistor and the current through it. Understanding this proportionality is fundamental to predicting how changes in supply voltage affect branch currents in simple and complex circuits alike.

Given Data / Assumptions:

• Resistor value R is constant and positive.
• Temperature and self-heating effects are negligible for the change considered.
• Polarity is fixed; we are discussing magnitude changes.

Concept / Approach:
Ohm’s law states V = I * R. Holding R constant implies I = V / R. Therefore, if V increases, I must increase proportionally. This is the definition of a linear, ohmic element. The exact numeric change requires R, but the qualitative direction (increase) does not.

Step-by-Step Solution:

Verification / Alternative check:
Plot I vs. V: the line I = (1/R) * V has positive slope 1/R. Any movement to the right along the V-axis moves up along the I-axis.

Why Other Options Are Wrong:

• Decreases/Stays the same: Contradicts I = V / R for constant R.
• Cannot be determined: While the exact value needs R, the trend is determined.
• Reverses direction: Direction is set by polarity; magnitude increase does not flip direction.

Common Pitfalls:
Confusing constant-current sources (which enforce I) with resistors (which follow Ohm’s law); ignoring that significant heating can change R slightly, but the ideal law remains linear.

Final Answer:
Increases