Core relationship in Ohm’s law Which statement correctly describes the proportionality between current and resistance when the applied voltage is held constant?
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Acurrent is inversely proportional to resistance
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Bresistance is directly proportional to voltage
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Cvoltage is indirectly proportional to power
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Dcurrent is directly proportional to resistance
Answer
Correct Answer: current is inversely proportional to resistance
Explanation
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