In a parallel circuit, if one branch has a resistance of 4Ω and another has 8Ω, what is the equivalent resistance? (2020)

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Q: In a parallel circuit, if one branch has a resistance of 4Ω and another has 8Ω, what is the equivalent resistance? (2020)

Solution: 1/R_eq = 1/4 + 1/8 = 2/8 + 1/8 = 3/8, so R_eq = 8/3Ω ≈ 2.67Ω.

Steps: 8

Step 1: Identify the resistances in the parallel circuit. We have one branch with a resistance of 4Ω and another with 8Ω.
Step 2: Write the formula for equivalent resistance in a parallel circuit: 1/R_eq = 1/R1 + 1/R2.
Step 3: Substitute the values into the formula: 1/R_eq = 1/4 + 1/8.
Step 4: Find a common denominator to add the fractions. The common denominator for 4 and 8 is 8.
Step 5: Convert 1/4 to have the common denominator: 1/4 = 2/8.
Step 6: Now add the fractions: 1/R_eq = 2/8 + 1/8 = 3/8.
Step 7: To find R_eq, take the reciprocal of 3/8: R_eq = 8/3Ω.
Step 8: Calculate 8/3 to get the approximate value: R_eq ≈ 2.67Ω.