Parallel resistors — equivalent resistance calculation: Find the total resistance of a parallel network with two resistors: 220 Ohm and 470 Ohm.

Introduction / Context:
Computing equivalent resistance for parallel resistors is a core skill. It is necessary for predicting current splits, source loading, and power dissipation in practical circuits.

Given Data / Assumptions:

• R1 = 220 Ohm.
• R2 = 470 Ohm.
• Ideal components, DC conditions.

Concept / Approach:
For two resistors in parallel, use R_eq = (R1 * R2) / (R1 + R2), which is an algebraic rearrangement of 1 / R_eq = 1 / R1 + 1 / R2. The equivalent must be less than the smallest individual resistance.

Step-by-Step Solution:
Compute numerator: R1 * R2 = 220 * 470 = 103,400.Compute denominator: R1 + R2 = 220 + 470 = 690.Divide: R_eq = 103,400 / 690 ≈ 149.855…Round suitably: ≈ 150 ohm.

Verification / Alternative check:
Using admittances: 1/220 ≈ 0.004545; 1/470 ≈ 0.002128; sum ≈ 0.006673 → R_eq ≈ 1 / 0.006673 ≈ 150 ohm. Both methods agree.

Why Other Options Are Wrong:
(a) 220 ohm is larger than the correct equivalent; (c) 445 ohm is near a series-like sum mistake; (d) 690 ohm is the series sum, not parallel; (e) is unnecessary as (b) is correct.

Common Pitfalls:
Forgetting that the equivalent of parallels is less than the smallest branch; arithmetic slips when multiplying and dividing.

Final Answer:
150 ohm.