Series-resistance concept check: When a fourth resistor is connected in series with an existing string of three resistors, how does the total circuit resistance change?

Introduction / Context:
Understanding how resistances combine is a core skill in circuit analysis. In series networks, resistances simply add. This conceptual item tests whether you recall that adding any positive resistance in series increases total resistance, thus reducing current for a fixed source voltage.

Given Data / Assumptions:

• Three resistors are already connected in series.
• A fourth resistor (with positive resistance) is added in series.
• No specific values are given; we reason qualitatively.

Concept / Approach:
The equivalent resistance of series elements is R_eq = R1 + R2 + R3 (+ R4 if added). Adding a positive term to a sum must increase the total. The phrase “increases by one-fourth” would only apply to a special case (all four resistors equal), which is not guaranteed here.

Step-by-Step Solution:

Verification / Alternative check:
Consider a numeric example: 10 Ω + 10 Ω + 10 Ω = 30 Ω. Add 5 Ω → 35 Ω, which is larger. With a fixed voltage V, the current I = V / R_eq decreases accordingly, confirming the qualitative conclusion.

Why Other Options Are Wrong:

• Increases by one-fourth: Not necessarily; only true if R4 equals the average of the existing three in a specific configuration (e.g., all equal).
• Decreases: Impossible when adding a positive series resistance.
• Remains the same: Also impossible unless R4 = 0 Ω (not stated).

Common Pitfalls:

• Confusing series with parallel rules (where adding a branch can reduce total resistance).
• Assuming equal values without explicit information.

Final Answer:
increases