Microampere estimation: Approximately how much current flows through a 3.3 MΩ resistor connected across a 30 V source?

Introduction / Context:
High-value resistors with modest voltages produce microampere-level currents. Estimating these currents is essential for leakage calculations, bias networks, and battery life projections in low-power designs.

Given Data / Assumptions:

• Resistance R = 3.3 MΩ = 3.3 × 10^6 Ω.
• Voltage V = 30 V.
• Need current magnitude I in microamperes.

Concept / Approach:
Ohm’s law gives I = V / R. Converting megaohms to ohms keeps arithmetic consistent; the expected answer is in the microampere range because V is in tens and R is in millions of ohms.

Step-by-Step Solution:

Verification / Alternative check:
Use the handy rule I(µA) ≈ V / R(MΩ). Here 30 / 3.3 ≈ 9.09 µA, which matches the computed value exactly, confirming the microampere estimate.

Why Other Options Are Wrong:

• 90 µA: Would require R ≈ 0.33 MΩ, ten times smaller.
• 900 µA: Corresponds to R ≈ 33 kΩ, far from 3.3 MΩ.
• 9000 µA: Implies R ≈ 3.3 kΩ, not megaohms.

Common Pitfalls:

• Confusing MΩ with kΩ and producing milliampere values by mistake.
• Not converting to microamperes after obtaining the ampere value.

Final Answer:
9 µA