What is the total resistance of two resistors of 4Ω and 6Ω connected in parallel

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Question: What is the total resistance of two resistors of 4Ω and 6Ω connected in parallel? (2021)

Options:

Correct Answer: 2.4Ω

Exam Year: 2021

Solution:

For parallel resistors, 1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/6. Finding a common denominator gives R_eq = 2.4Ω.

What is the total resistance of two resistors of 4Ω and 6Ω connected in parallel? (2021)

What is the total resistance of two resistors of 4Ω and 6Ω connected in parallel? (2021)

Step 1: Identify the values of the resistors. We have R1 = 4Ω and R2 = 6Ω.
Step 2: Use the formula for total resistance in parallel: 1/R_eq = 1/R1 + 1/R2.
Step 3: Substitute the values into the formula: 1/R_eq = 1/4 + 1/6.
Step 4: Find a common denominator for the fractions. The common denominator for 4 and 6 is 12.
Step 5: Rewrite the fractions with the common denominator: 1/4 = 3/12 and 1/6 = 2/12.
Step 6: Add the fractions: 1/R_eq = 3/12 + 2/12 = 5/12.
Step 7: To find R_eq, take the reciprocal of 5/12: R_eq = 12/5.
Step 8: Calculate 12/5, which equals 2.4Ω.

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