Very high resistance with modest voltage: a 3.3 MΩ resistor is placed across a 500 V source. Estimate the resulting current and select the closest microampere value.

Introduction / Context:Leakage and bias currents in high-value resistor networks are often in the microampere range. Converting megaohms and volts into current with Ohm’s law is a staple calculation in instrumentation and high-impedance circuits.

Given Data / Assumptions:

• R = 3.3 MΩ = 3.3 × 10^6 Ω.
• V = 500 V.
• Compute I = V / R and express in µA.

Concept / Approach:

Use the base SI units to avoid confusion: volts divided by ohms yields amperes. Then scale to microamperes by multiplying by 10^6.

Step-by-Step Solution:

Verification / Alternative check:

Prefix method: 500 V / 3.3 MΩ ≈ (500/3.3) × 10^-6 A ≈ 151.5 µA, consistent with the calculation.

Why Other Options Are Wrong:

15.1 µA is 10× too small; 66 mA and 660 mA are far too large for megaohm resistances at 500 V.

Common Pitfalls:

Dropping the 10^6 factor for mega; mixing milliamps and microamps.

Final Answer:

151 µA