Equal resistors in series with a 12 V battery: Four identical resistors in series draw 13.63 mA. What is the resistance value of each individual resistor?

Introduction / Context:
Determining component values from measured current and source voltage is a routine application of Ohm's law. With identical series resistors, the total resistance is an integer multiple of one resistor, simplifying calculations and offering a quick consistency check.

Given Data / Assumptions:

• Battery voltage V = 12 V (DC).
• Total current I = 13.63 mA = 0.01363 A.
• Four equal-value resistors in series; call each R.

Concept / Approach:
Total resistance is R_total = 4R. Use R_total = V / I to find the combined resistance, then divide by 4 to obtain each resistor's value. Keep sufficient significant figures before rounding to the nearest offered option.

Step-by-Step Solution:

Verification / Alternative check:
Back-calculate current using 4 × 220 Ω = 880 Ω: I = 12 / 880 = 0.013636… A = 13.636 mA, which matches the given 13.63 mA within rounding. Power per resistor P = I^2 * R ≈ (0.01363)^2 * 220 ≈ 0.0409 W, safe for 1/8 W parts.

Why Other Options Are Wrong:

• 22 Ω or 88 Ω: Would give total resistance far too small, producing much larger currents.
• 880 Ω: That is the total, not each resistor. Choosing this confuses per-element value with the overall series sum.

Common Pitfalls:

• Forgetting to divide the total by the number of equal resistors.
• Rounding intermediate values too early, causing noticeable discrepancy.

Final Answer:
220 Ω