Series circuits — assess the statement: “The total resistance of a series circuit equals the average (arithmetic mean) of all individual resistance values.” Is this claim valid for ideal series connections?

Introduction / Context:
Understanding how resistances combine is foundational for circuit analysis. In a series circuit, there is a single path for current, and each resistor shares the same current. This question challenges a common misconception: that the total series resistance equals the average of the resistor values, rather than the sum. Clarifying this point prevents systematic errors in design and troubleshooting.

Given Data / Assumptions:

• Ideal lumped components (no parasitic effects).
• Resistors R1, R2, …, Rn connected in series (one current path).
• Goal: compare “sum” versus “average” for total resistance.

Concept / Approach:
Kirchhoff’s Voltage Law (KVL) states that the sum of voltage drops around a loop equals the source voltage. With a common current I in a series chain, the total voltage drop is I*R1 + I*R2 + … + I*Rn. Equating with V = I*R_total directly yields R_total = R1 + R2 + … + Rn. An average would be (R1 + … + Rn) / n, which underestimates the real series total whenever n > 1 (unless all but one are zero, which is not a useful physical case).

Step-by-Step Solution:

Verification / Alternative check:
Take a numeric example: R1 = 10 Ω, R2 = 20 Ω. Sum = 30 Ω. Average = 15 Ω. Measuring current with a fixed source shows the 30 Ω result matches I = V / 30, not V / 15, confirming that average is incorrect.

Why Other Options Are Wrong:

• Correct: Conflicts with R_total = sum of series resistances.
• Applies only when all resistors are equal: Even then, the total is n*R, not the average R.
• Applies only below 1 kΩ: Resistance combination rules are not value-range dependent.

Common Pitfalls:
Confusing series (resistances add) with parallel (conductances add); thinking “average” because of evenly shared current. Series totals always add arithmetically.

Final Answer:
Incorrect — total series resistance is the sum, not the average.