What is the total resistance in a parallel circuit with two resistors of 4 ohms

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Question: What is the total resistance in a parallel circuit with two resistors of 4 ohms and 6 ohms?

Options:

Correct Answer: 2.4 ohms

Solution:

The total resistance (R_total) in parallel is given by 1/R_total = 1/R1 + 1/R2. Thus, 1/R_total = 1/4 + 1/6 = 5/12, so R_total = 12/5 = 2.4 ohms.

What is the total resistance in a parallel circuit with two resistors of 4 ohms and 6 ohms?

What is the total resistance in a parallel circuit with two resistors of 4 ohms and 6 ohms?

Step 1: Identify the resistors in the parallel circuit. We have R1 = 4 ohms and R2 = 6 ohms.
Step 2: Write the formula for total resistance in a parallel circuit: 1/R_total = 1/R1 + 1/R2.
Step 3: Substitute the values of R1 and R2 into the formula: 1/R_total = 1/4 + 1/6.
Step 4: Find a common denominator to add 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_total = 3/12 + 2/12 = 5/12.
Step 7: To find R_total, take the reciprocal of 5/12: R_total = 12/5.
Step 8: Calculate 12/5 to get the final answer: R_total = 2.4 ohms.

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