Parallel resistors – total equivalent resistance calculation: What is the total resistance of four identical resistors, each 1 kΩ, when they are connected in parallel?

Introduction / Context:
Calculating the equivalent resistance of parallel-connected resistors is a foundational skill in circuit analysis. It is frequently used in designing bias networks, sensor interfaces, and power distribution where lower equivalent resistance or higher current capability is needed.

Given Data / Assumptions:

• There are 4 identical resistors.
• Each resistor value R = 1 kΩ.
• Connection is purely parallel; leads and source resistances are neglected.

Concept / Approach:
For n identical resistors in parallel, the equivalent resistance is R_eq = R / n. More generally, for parallel branches the conductances add: 1 / R_eq = 1 / R_1 + 1 / R_2 + ... + 1 / R_n.

Step-by-Step Solution:
Identify n = 4, R = 1 kΩ.Use identical-parallel shortcut: R_eq = R / n.Compute: R_eq = 1 kΩ / 4 = 0.25 kΩ.Convert to ohms: 0.25 kΩ = 250 Ω.

Verification / Alternative check:
Using the full formula: 1/R_eq = 1/1000 + 1/1000 + 1/1000 + 1/1000 = 4/1000 = 0.004; hence R_eq = 1 / 0.004 = 250 Ω.

Why Other Options Are Wrong:

• 200 Ω and 400 Ω: do not match R/4 for identical 1 kΩ branches.
• 4 kΩ or 1 kΩ: these are typical of series or single-branch values, not four-way parallel.

Common Pitfalls:
Mixing series and parallel rules, or forgetting that equivalent resistance in parallel must be less than the smallest branch resistance.

Final Answer:
250 ohms