In a parallel circuit with three resistors R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω, what is the equivalent resistance?

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Q: In a parallel circuit with three resistors R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω, what is the equivalent resistance?

Solution: The equivalent resistance in parallel is given by 1/R_total = 1/R1 + 1/R2 + 1/R3. Thus, 1/R_total = 1/2 + 1/3 + 1/6 = 1Ω.

Steps: 8

Step 1: Identify the resistors in the parallel circuit. We have R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω.
Step 2: Write the formula for equivalent resistance in a parallel circuit: 1/R_total = 1/R1 + 1/R2 + 1/R3.
Step 3: Substitute the values of the resistors into the formula: 1/R_total = 1/2 + 1/3 + 1/6.
Step 4: Find a common denominator for the fractions. The common denominator for 2, 3, and 6 is 6.
Step 5: Rewrite each fraction with the common denominator: 1/2 = 3/6, 1/3 = 2/6, and 1/6 = 1/6.
Step 6: Add the fractions together: 3/6 + 2/6 + 1/6 = 6/6.
Step 7: Simplify the sum: 6/6 = 1.
Step 8: Since 1/R_total = 1, we find R_total = 1Ω.