In a parallel circuit with two resistors of 4Ω and 12Ω, what is the total curren

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

Options:

Correct Answer: 8A

Exam Year: 2022

Solution:

First, find the equivalent resistance: 1/R_eq = 1/4 + 1/12 = 3/12 + 1/12 = 4/12, R_eq = 3Ω. Then, I = V/R_eq = 24V / 3Ω = 8A.

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

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

Step 1: Identify the resistors in the parallel circuit. We have two resistors: one is 4Ω and the other is 12Ω.
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 + 1/12.
Step 4: Find a common denominator to add the fractions. The common denominator for 4 and 12 is 12.
Step 5: Rewrite the fractions: 1/4 = 3/12 and 1/12 = 1/12.
Step 6: Add the fractions: 1/R_eq = 3/12 + 1/12 = 4/12.
Step 7: Invert the fraction to find R_eq: R_eq = 12/4 = 3Ω.
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 = 24V / 3Ω.
Step 10: Calculate the total current: I = 8A.

Parallel Circuit Resistance – Understanding how to calculate the equivalent resistance in a parallel circuit using the formula 1/R_eq = 1/R1 + 1/R2.
Ohm's Law – Applying Ohm's Law (I = V/R) to find the total current in the circuit after determining the equivalent resistance.