Ohm’s law proportional change — repaired stem: In a fixed-resistance DC circuit, the current is initially 8 mA. If the current is increased to 24 mA with the same resistance, the source voltage must have tripled. Evaluate this claim.

Introduction / Context:This item originally referenced a “given circuit” without data. Applying the Recovery-First Policy, we minimally repaired the stem by stating the initial current explicitly and assuming a fixed-resistance DC circuit. The concept being tested is the direct proportionality between current and voltage for a constant resistance, as stated by Ohm’s law.

Given Data / Assumptions:

• Initial current I1 = 8 mA.
• Final current I2 = 24 mA.
• Resistance R is constant (temperature and tolerance effects neglected).
• DC source; wires and contacts ideal for concept.

Concept / Approach:Ohm’s law gives I = V / R or equivalently V = I * R. With R fixed, voltage and current are directly proportional. Therefore, any multiplicative change in current requires the same multiplicative change in voltage. Tripling the current requires tripling the voltage at constant resistance.

Step-by-Step Solution:

Verification / Alternative check:Numerical example: If R = 1 kΩ, then V1 = 8 mA * 1 kΩ = 8 V and V2 = 24 mA * 1 kΩ = 24 V, confirming a 3x increase. The specific R cancels in the ratio, so the conclusion does not depend on its value.

Why Other Options Are Wrong:

• Incorrect: Conflicts with direct proportionality at constant resistance.
• Only correct for AC sources: The proportionality holds for DC and RMS AC in resistive circuits.
• Only correct if resistance decreases: Resistance is specified constant; no change is required or implied.

Common Pitfalls:Forgetting to specify that resistance is constant; mixing peak and RMS when dealing with AC; assuming the conclusion depends on a particular resistance value when the ratio makes it independent.

Final Answer:Correct.