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In a parallel circuit with three resistors of 2Ω, 3Ω, and 6Ω, what is the equiva

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Question: In a parallel circuit with three resistors of 2Ω, 3Ω, and 6Ω, what is the equivalent resistance?

Options:

  1. 1Ω
  2. 2Ω
  3. 3Ω
  4. 4Ω

Correct Answer: 2Ω

Solution: 

The equivalent resistance for resistors in parallel is given by 1/R_eq = 1/R1 + 1/R2 + 1/R3. Thus, 1/R_eq = 1/2 + 1/3 + 1/6 = 1. Therefore, R_eq = 1Ω.

In a parallel circuit with three resistors of 2Ω, 3Ω, and 6Ω, what is the equiva

Practice Questions

Q1
In a parallel circuit with three resistors of 2Ω, 3Ω, and 6Ω, what is the equivalent resistance?
  1. 1Ω
  2. 2Ω
  3. 3Ω
  4. 4Ω

Questions & Step-by-Step Solutions

In a parallel circuit with three resistors of 2Ω, 3Ω, and 6Ω, what is the equivalent resistance?
Correct Answer: 1Ω
  • Step 1: Identify the resistors in the parallel circuit. We have three resistors: R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω.
  • Step 2: Write 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 = 1/2 + 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: Now, we have 1/R_eq = 1, so we can find R_eq by taking the reciprocal: R_eq = 1Ω.
  • Equivalent Resistance in Parallel Circuits – Understanding how to calculate the total resistance when multiple resistors are connected in parallel.
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