A circuit contains a 12V battery and two resistors of 4Ω and 6Ω in parallel. Wha

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Question: A circuit contains a 12V battery and two resistors of 4Ω and 6Ω in parallel. What is the total current supplied by the battery? (2019)

Options:

Correct Answer: 3 A

Exam Year: 2019

Solution:

First, find the equivalent resistance R_eq = 1/(1/4 + 1/6) = 2.4Ω. Then, I = V/R_eq = 12V/2.4Ω = 5 A.

A circuit contains a 12V battery and two resistors of 4Ω and 6Ω in parallel. What is the total current supplied by the battery? (2019)

A circuit contains a 12V battery and two resistors of 4Ω and 6Ω in parallel. What is the total current supplied by the battery? (2019)

Step 1: Identify the values given in the problem. We have a 12V battery and two resistors: one is 4Ω and the other is 6Ω.
Step 2: Understand that the resistors are in parallel. This means we need to find the equivalent resistance (R_eq) using the formula for parallel resistors.
Step 3: Use the formula for equivalent resistance in parallel: R_eq = 1 / (1/R1 + 1/R2). Here, R1 is 4Ω and R2 is 6Ω.
Step 4: Calculate 1/R1 and 1/R2: 1/4 = 0.25 and 1/6 ≈ 0.1667.
Step 5: Add these two values together: 0.25 + 0.1667 = 0.4167.
Step 6: Take the reciprocal of the sum to find R_eq: R_eq = 1 / 0.4167 ≈ 2.4Ω.
Step 7: Now, use Ohm's Law to find the total current (I) supplied by the battery. The formula is I = V / R_eq.
Step 8: Substitute the values into the formula: I = 12V / 2.4Ω.
Step 9: Calculate the current: I = 5 A.

Ohm's Law – The relationship between voltage, current, and resistance in an electrical circuit, expressed as V = I * R.
Equivalent Resistance in Parallel Circuits – The method to calculate the total resistance of resistors connected in parallel, using the formula 1/R_eq = 1/R1 + 1/R2.