In a circuit with a 24V battery and three resistors in parallel (4Ω, 6Ω, and 12Ω), what is the total current supplied by the battery?

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Q: In a circuit with a 24V battery and three resistors in parallel (4Ω, 6Ω, and 12Ω), what is the total current supplied by the battery?

Solution: 1/R_eq = 1/4 + 1/6 + 1/12 = 1. Therefore, R_eq = 2Ω. Total current I = V/R_eq = 24V/2Ω = 12A.

Steps: 9

Step 1: Identify the resistors in the circuit. We have three resistors: 4Ω, 6Ω, and 12Ω.
Step 2: Use the formula for total resistance in parallel: 1/R_eq = 1/R1 + 1/R2 + 1/R3.
Step 3: Substitute the values of the resistors into the formula: 1/R_eq = 1/4 + 1/6 + 1/12.
Step 4: Calculate each term: 1/4 = 0.25, 1/6 ≈ 0.1667, and 1/12 ≈ 0.0833.
Step 5: Add the values together: 0.25 + 0.1667 + 0.0833 = 0.5.
Step 6: Take the reciprocal to find R_eq: R_eq = 1/0.5 = 2Ω.
Step 7: Use Ohm's law to find the total current: I = V/R_eq.
Step 8: Substitute the values: I = 24V / 2Ω.
Step 9: Calculate the total current: I = 12A.