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What is the equivalent resistance of three resistors of values 2Ω, 3Ω, and 6Ω co
What is the equivalent resistance of three resistors of values 2Ω, 3Ω, and 6Ω connected in parallel?
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Q1
What is the equivalent resistance of three resistors of values 2Ω, 3Ω, and 6Ω connected in parallel?
1Ω
2Ω
3Ω
4Ω
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1/Req = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/6 = 1. Therefore, Req = 1Ω.
Questions & Step-by-step Solutions
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Q
Q: What is the equivalent resistance of three resistors of values 2Ω, 3Ω, and 6Ω connected in parallel?
Solution:
1/Req = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/6 = 1. Therefore, Req = 1Ω.
Steps: 8
Show Steps
Step 1: Identify the values of the resistors. We have R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω.
Step 2: Use the formula for equivalent resistance in parallel: 1/Req = 1/R1 + 1/R2 + 1/R3.
Step 3: Substitute the values into the formula: 1/Req = 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: 1/Req = 3/6 + 2/6 + 1/6 = 6/6.
Step 7: Simplify the sum: 6/6 = 1.
Step 8: Take the reciprocal to find Req: Req = 1Ω.
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