In a parallel circuit with three resistors of 6 ohms, 12 ohms, and 18 ohms, what is the equivalent resistance?

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Q: In a parallel circuit with three resistors of 6 ohms, 12 ohms, and 18 ohms, what is the equivalent resistance?

Solution: Using the formula for resistors in parallel, 1/R_eq = 1/R1 + 1/R2 + 1/R3, we find R_eq = 1 / (1/6 + 1/12 + 1/18) = 3 ohms.

Steps: 7

Step 1: Identify the resistors in the parallel circuit. We have three resistors: R1 = 6 ohms, R2 = 12 ohms, and R3 = 18 ohms.
Step 2: Write down the formula for equivalent resistance in a parallel circuit: 1/R_eq = 1/R1 + 1/R2 + 1/R3.
Step 3: Substitute the values of the resistors into the formula: 1/R_eq = 1/6 + 1/12 + 1/18.
Step 4: Calculate each term on the right side of the equation: 1/6 = 0.1667, 1/12 = 0.0833, and 1/18 = 0.0556.
Step 5: Add these values together: 0.1667 + 0.0833 + 0.0556 = 0.3056.
Step 6: Now, take the reciprocal of the sum to find R_eq: R_eq = 1 / 0.3056.
Step 7: Calculate the final value: R_eq ≈ 3 ohms.