In a parallel circuit with two resistors of 6Ω and 3Ω, what is the total current

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Question: In a parallel circuit with two resistors of 6Ω and 3Ω, what is the total current if a 12V battery is connected? (2021)

Options:

Correct Answer: 6A

Exam Year: 2021

Solution:

First, find the equivalent resistance: 1/R_eq = 1/6 + 1/3 = 1/2, so R_eq = 2Ω. Then, I = V/R_eq = 12V / 2Ω = 6A.

In a parallel circuit with two resistors of 6Ω and 3Ω, what is the total current if a 12V battery is connected? (2021)

In a parallel circuit with two resistors of 6Ω and 3Ω, what is the total current if a 12V battery is connected? (2021)

Step 1: Identify the resistors in the parallel circuit. We have two resistors: one is 6Ω and the other is 3Ω.
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 = 1/6 + 1/3.
Step 4: Find a common denominator to add the fractions. The common denominator for 6 and 3 is 6.
Step 5: Rewrite 1/3 as 2/6, so now we have: 1/R_eq = 1/6 + 2/6 = 3/6.
Step 6: Simplify 3/6 to 1/2, so we have 1/R_eq = 1/2.
Step 7: To find R_eq, take the reciprocal of 1/2, which gives us R_eq = 2Ω.
Step 8: Now, use Ohm's Law to find the total current. The formula is I = V/R_eq.
Step 9: Substitute the values: I = 12V / 2Ω.
Step 10: Calculate the 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.