Voltage requirement by Ohm’s law: What voltage is needed to drive 2.5 A through a 200 Ω resistor (assume steady DC)?

Introduction / Context:
Determining the required supply voltage for a specified current through a known resistance is a routine design step. It ensures the source and insulation ratings are adequate for the intended load current and power dissipation.

Given Data / Assumptions:

• Resistance R = 200 Ω.
• Desired current I = 2.5 A.
• Find voltage V that satisfies Ohm’s law under DC conditions.

Concept / Approach:
Use the voltage form of Ohm’s law, V = I * R. After computing V, it is wise to evaluate power to judge component stress, since high current through a large resistance implies significant heat.

Step-by-Step Solution:

Verification / Alternative check:
Power check: P = I^2 * R = (2.5)^2 * 200 = 6.25 * 200 = 1250 W. Also P = V * I = 500 * 2.5 = 1250 W. Agreement confirms the calculation and highlights that this scenario demands very high power handling.

Why Other Options Are Wrong:

• 50 V: Would produce I = 0.25 A, ten times smaller.
• 80 V: Gives I = 0.4 A, well below 2.5 A.
• 8 V: Gives I = 0.04 A, far too small.

Common Pitfalls:

• Dismissing the power implications; a 200 Ω load at 2.5 A is a kilowatt-class burden.
• Transposing digits when multiplying, leading to 50 V instead of 500 V.

Final Answer:
500 V