What is the equivalent resistance of two resistors, 3Ω and 6Ω, in parallel?

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Question: What is the equivalent resistance of two resistors, 3Ω and 6Ω, in parallel?

Options:

Correct Answer: 4Ω

Solution:

The formula for equivalent resistance in parallel is 1/R_eq = 1/R1 + 1/R2. Thus, 1/R_eq = 1/3 + 1/6 = 1/2, so R_eq = 2Ω.

What is the equivalent resistance of two resistors, 3Ω and 6Ω, in parallel?

What is the equivalent resistance of two resistors, 3Ω and 6Ω, in parallel?

Step 1: Identify the resistors. We have two resistors: R1 = 3Ω and R2 = 6Ω.
Step 2: Write down the formula for equivalent resistance in parallel: 1/R_eq = 1/R1 + 1/R2.
Step 3: Substitute the values of R1 and R2 into the formula: 1/R_eq = 1/3 + 1/6.
Step 4: Find a common denominator to add the fractions. The common denominator for 3 and 6 is 6.
Step 5: Rewrite 1/3 as 2/6, so now we have: 1/R_eq = 2/6 + 1/6.
Step 6: Add the fractions: 1/R_eq = (2 + 1)/6 = 3/6.
Step 7: Simplify 3/6 to 1/2, so we have: 1/R_eq = 1/2.
Step 8: To find R_eq, take the reciprocal of 1/2: R_eq = 2Ω.

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