Using Ohm’s law in basic circuit analysis: What is the approximate resistance setting of a rheostat if a current of 650 mA flows from a 150 V source?

Introduction / Context:
This problem checks fast application of Ohm’s law to determine an unknown resistance when the source voltage and the circuit current are known. Such estimates are common when setting a rheostat to limit current to a safe value in laboratory benches and troubleshooting.

Given Data / Assumptions:

• Source voltage V = 150 V (direct current conditions assumed).
• Measured current I = 650 mA = 0.65 A.
• Ideal lumped resistance model; temperature effects and rheostat tolerance ignored.

Concept / Approach:
Use Ohm’s law to relate the three variables: V = I * R. Solving for resistance gives R = V / I. Keep track of units by converting milliamperes to amperes before substitution to avoid thousandfold errors.

Step-by-Step Solution:

Verification / Alternative check:
Back substitute to sanity-check: I = V / R ≈ 150 / 230 ≈ 0.652 A ≈ 652 mA, which is essentially the stated 650 mA once rounding is considered. The direction and magnitude are consistent.

Why Other Options Are Wrong:

• 9.7 Ω: Would draw I ≈ 150 / 9.7 ≈ 15.5 A, far too large.
• 97 Ω: Gives I ≈ 1.55 A, still much larger than 0.65 A.
• 23 Ω: Gives I ≈ 6.5 A, an order of magnitude high.

Common Pitfalls:

• Forgetting to convert 650 mA to 0.65 A before computing R.
• Rounding too early; compute first, then pick the closest option.

Final Answer:
230 Ω