What is the total current in a circuit with a 12V battery and three resistors (R1 = 4Ω, R2 = 4Ω, R3 = 4Ω) connected in parallel?
Practice Questions
1 question
Q1
What is the total current in a circuit with a 12V battery and three resistors (R1 = 4Ω, R2 = 4Ω, R3 = 4Ω) connected in parallel?
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Total resistance R_eq = 1 / (1/R1 + 1/R2 + 1/R3) = 1 / (1/4 + 1/4 + 1/4) = 1.33Ω. Current I = V / R_eq = 12V / 1.33Ω ≈ 9A.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the total current in a circuit with a 12V battery and three resistors (R1 = 4Ω, R2 = 4Ω, R3 = 4Ω) connected in parallel?
Solution: Total resistance R_eq = 1 / (1/R1 + 1/R2 + 1/R3) = 1 / (1/4 + 1/4 + 1/4) = 1.33Ω. Current I = V / R_eq = 12V / 1.33Ω ≈ 9A.
Steps: 8
Step 1: Identify the values given in the problem. We have a 12V battery and three resistors, each with a resistance of 4Ω.
Step 2: Since the resistors are connected in parallel, we need to calculate the total resistance (R_eq) using the formula: 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 + 1/4 + 1/4.
Step 4: Calculate the right side of the equation: 1/4 + 1/4 + 1/4 = 3/4.
Step 5: Now, take the reciprocal to find R_eq: R_eq = 1 / (3/4) = 4/3 = 1.33Ω.
Step 6: Now that we have the total resistance, we can find the total current (I) using Ohm's Law: I = V / R_eq.
Step 7: Substitute the values into the formula: I = 12V / 1.33Ω.
