In a parallel circuit with two resistors of 4Ω and 12Ω, what is the total current if the voltage across them is 24V? (2022)

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Q: In a parallel circuit with two resistors of 4Ω and 12Ω, what is the total current if the voltage across them is 24V? (2022)

Solution: Total current I = V/R_eq. First, find R_eq = 1/(1/4 + 1/12) = 3Ω. Then, I = 24V / 3Ω = 8A.

Steps: 9

Step 1: Identify the resistors in the parallel circuit. We have two resistors: one is 4Ω and the other is 12Ω.
Step 2: Write down the formula to find the equivalent resistance (R_eq) for resistors in parallel: R_eq = 1 / (1/R1 + 1/R2).
Step 3: Substitute the values of the resistors into the formula: R_eq = 1 / (1/4 + 1/12).
Step 4: Calculate 1/4 and 1/12. 1/4 = 0.25 and 1/12 = 0.0833.
Step 5: Add these two values together: 0.25 + 0.0833 = 0.3333.
Step 6: Take the reciprocal of the sum to find R_eq: R_eq = 1 / 0.3333 = 3Ω.
Step 7: Now, use the total voltage (V = 24V) and the equivalent resistance (R_eq = 3Ω) to find the total current (I) using the formula: I = V / R_eq.
Step 8: Substitute the values into the formula: I = 24V / 3Ω.
Step 9: Calculate the total current: I = 8A.