5Lena, a high school student in the STEM program, is designing a circuit with three resistors in parallel. The resistances are \(12 \, \Omega\), \(6 \, \Omega\), and \(4 \, \Omega\). What is the total resistance of the circuit in ohms?

["Title: How to Calculate Total Resistance in a Parallel Circuit: A High School STEM Project Breakdown", "When tackling complex circuit problems in high school STEM programs, understanding how to calculate total resistance in parallel resistors is essential. One exciting project involves designing a circuit with three resistors—(12, \Omega), (6, \Omega), and (4, \Omega)—connected in parallel. If you're working on a STEM project like this and wondering, “What is the total resistance of the circuit?”, you’re in the right place. Here’s a clear, step-by-step explanation.", "### Understanding Parallel Resistors\nIn a parallel circuit, the voltage across each resistor is the same, but the current divides. The total conductance (reciprocal of resistance) adds up, then inversely converts back to total resistance. This is more efficient in STEM labs because it allows controlled current flow while minimizing power loss—perfect for hands-on experiments.", "### The Formula for Parallel Resistors\nFor resistors in parallel, the total resistance ( R_{\ ext{total}} ) is calculated using:\n[\n\frac{1}{R_{\ ext{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\n]\nSubstituting the given values:\n[\n\frac{1}{R_{\ ext{total}}} = \frac{1}{12} + \frac{1}{6} + \frac{1}{4}\n]", "### Step-by-Step Calculation\n1. Find common denominator: The least common multiple of 12, 6, and 4 is 12.\n2. Rewrite fractions:\n [\n \frac{1}{12} + \frac{2}{12} + \frac{3}{12} = \frac{6}{12}\n ]\n3. Simplify:\n [\n \frac{1}{R_{\ ext{total}}} = \frac{6}{12} = \frac{1}{2}\n ]\n4. Solve for ( R_{\ ext{total}} ):\n [\n R_{\ ext{total}} = 2, \Omega\n ]", "### Why This Matters in STEM\nThis calculation demonstrates key principles of parallel circuits, reinforcing concepts like Ohm’s Law and resistive division. For STEM students, mastering this formula builds the foundation for designing safe, efficient circuits in robotics, electronics, and renewable energy projects.", "### Final Answer\nThe total resistance of the three resistors ((12, \Omega), (6, \Omega), and (4, \Omega)) in parallel is (2, \Omega).", "By working through problems like this, high school STEM learners strengthen their analytical and problem-solving skills—preparing them for deeper exploration in physics, engineering, and innovation.", "---\nKeywords: total resistance parallel resistors, STEM project resistors, Lena circuit calculation, high school physics, parallel circuit formula, STEM electric circuit design."]