In a parallel circuit with two resistors of 4Ω and 6Ω, what is the total current if the voltage across the circuit is 12V?

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Q: In a parallel circuit with two resistors of 4Ω and 6Ω, what is the total current if the voltage across the circuit is 12V?

Solution: First, find the equivalent resistance: 1/R_eq = 1/4 + 1/6 => R_eq = 2.4Ω. Then, I = V/R_eq = 12V / 2.4Ω = 5A.

Steps: 10

Step 1: Identify the resistors in the parallel circuit. We have two resistors: one is 4Ω and the other is 6Ω.
Step 2: Use the formula for equivalent resistance in a parallel circuit: 1/R_eq = 1/R1 + 1/R2.
Step 3: Substitute the values of the resistors into the formula: 1/R_eq = 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: 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: Invert the fraction to find R_eq: R_eq = 12/5 = 2.4Ω.
Step 8: Use Ohm's Law to find the total current: I = V/R_eq.
Step 9: Substitute the voltage and equivalent resistance into the formula: I = 12V / 2.4Ω.
Step 10: Calculate the total current: I = 5A.