Core relationship in Ohm’s law Which statement correctly describes the proportionality between current and resistance when the applied voltage is held constant?

Introduction / Context:
Ohm’s law is the cornerstone of basic circuit analysis. It defines a simple linear relationship among voltage, current, and resistance, allowing quick predictions of how one variable changes when another is adjusted.

Given Data / Assumptions:

• Ohmic components and linear operating region.
• Applied voltage is constant.
• Temperature and material properties assumed stable.

Concept / Approach:
Ohm’s law: V = I * R. Solving for current yields I = V / R. With V fixed, it is clear that current varies inversely with resistance: doubling R halves I; halving R doubles I. This inverse proportionality is fundamental to resistor networks and load-line analysis.

Step-by-Step Solution:
Start from V = I * R.Hold V constant and isolate I: I = V / R.Observe: I is proportional to 1/R.Therefore, current is inversely proportional to resistance at constant voltage.

Verification / Alternative check:
Plot I versus R for fixed V: a rectangular hyperbola passing through (R, I) pairs such as (1 kΩ, 10 mA) and (2 kΩ, 5 mA).

Why Other Options Are Wrong:
Resistance directly proportional to voltage: not a general law; R is material/geometry dependent.Voltage indirectly proportional to power: mixing relationships; power depends on both V and I.Current directly proportional to resistance: contradicts I = V / R.

Common Pitfalls:
Ignoring temperature dependence in real resistors; at high power, R may change, but the law’s proportionality at a given instant still applies.

Final Answer:
current is inversely proportional to resistance