Many-equal-resistor parallel network: Fifteen resistors, each of value 2 MΩ, are all connected in parallel. What is the total equivalent resistance RT of the combination?

Introduction / Context:Equal-value resistors in parallel reduce to a simple formula that is frequently used in bias networks and sensor arrays. This question reinforces the shortcut and careful unit handling from megaohms to kiloohms.

Given Data / Assumptions:

• N = 15 identical resistors.
• Each resistor R = 2 MΩ.
• Ideal DC behavior.

Concept / Approach:For N equal resistors in parallel, RT = R / N. This follows from adding conductances, since total conductance G_total = N * (1/R).

Step-by-Step Solution:RT = R / N = 2 MΩ / 15.Compute numeric value: 2,000,000 Ω / 15 ≈ 133,333.33 Ω.Express in kiloohms: ≈ 133 kΩ.

Verification / Alternative check:Check conductance: each is 0.5 µS (since 1 / 2 MΩ). Times 15 gives 7.5 µS. Equivalent resistance is 1 / 7.5 µS ≈ 133.3 kΩ. Matches the result.

Why Other Options Are Wrong:300 kΩ and 750 kΩ correspond to incorrect division or mixing units; 30 MΩ is larger than a single branch and cannot be the parallel result.

Common Pitfalls:Forgetting that parallel decreases resistance; mis-converting megaohms to kiloohms leading to order-of-magnitude errors.

Final Answer:133 kΩ