In a parallel circuit with two resistors (4Ω and 6Ω), what is the total resistan

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Question: In a parallel circuit with two resistors (4Ω and 6Ω), what is the total resistance?

Options:

Correct Answer: 2.4Ω

Solution:

Total resistance R = 1 / (1/R1 + 1/R2) = 1 / (1/4 + 1/6) = 1 / (3/12 + 2/12) = 1 / (5/12) = 12/5 = 2.4Ω.

In a parallel circuit with two resistors (4Ω and 6Ω), what is the total resistance?

In a parallel circuit with two resistors (4Ω and 6Ω), what is the total resistance?

Step 1: Identify the resistors in the parallel circuit. We have R1 = 4Ω and R2 = 6Ω.
Step 2: Use the formula for total resistance in a parallel circuit: R = 1 / (1/R1 + 1/R2).
Step 3: Substitute the values of R1 and R2 into the formula: R = 1 / (1/4 + 1/6).
Step 4: Find a common denominator for the fractions 1/4 and 1/6. The common denominator is 12.
Step 5: Convert 1/4 to 3/12 and 1/6 to 2/12.
Step 6: Add the two fractions: 3/12 + 2/12 = 5/12.
Step 7: Now substitute back into the formula: R = 1 / (5/12).
Step 8: To divide by a fraction, multiply by its reciprocal: R = 1 * (12/5).
Step 9: Calculate the result: R = 12/5 = 2.4Ω.

Parallel Circuit Resistance Calculation – Understanding how to calculate total resistance in a parallel circuit using the formula R_total = 1 / (1/R1 + 1/R2).