In a parallel circuit with two resistors of 8Ω and 4Ω, what is the total current

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Question: In a parallel circuit with two resistors of 8Ω and 4Ω, what is the total current if the voltage across the circuit is 16V? (2022)

Options:

Correct Answer: 8A

Exam Year: 2022

Solution:

First, find the equivalent resistance: 1/R_eq = 1/8 + 1/4 = 1/8 + 2/8 = 3/8, so R_eq = 8/3Ω. Then, I = V/R_eq = 16V / (8/3)Ω = 16 * 3/8 = 6A.

In a parallel circuit with two resistors of 8Ω and 4Ω, what is the total current if the voltage across the circuit is 16V? (2022)

In a parallel circuit with two resistors of 8Ω and 4Ω, what is the total current if the voltage across the circuit is 16V? (2022)

Step 1: Identify the resistors in the parallel circuit. We have two resistors: one is 8Ω and the other is 4Ω.
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 = 1/8 + 1/4.
Step 4: Convert 1/4 to have a common denominator with 1/8: 1/4 = 2/8.
Step 5: Now add the fractions: 1/R_eq = 1/8 + 2/8 = 3/8.
Step 6: To find R_eq, take the reciprocal of 3/8: R_eq = 8/3Ω.
Step 7: Use Ohm's Law to find the total current: I = V/R_eq.
Step 8: Substitute the voltage (16V) and the equivalent resistance (8/3Ω) into the formula: I = 16V / (8/3Ω).
Step 9: Simplify the equation: I = 16 * (3/8).
Step 10: Calculate the total current: I = 6A.

Parallel Circuit Resistance – Understanding how to calculate 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.