In a circuit with a 24V battery and two resistors of 4Ω and 8Ω in parallel, what

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Question: In a circuit with a 24V battery and two resistors of 4Ω and 8Ω in parallel, what is the total current supplied by the battery? (2022)

Options:

Correct Answer: 6A

Exam Year: 2022

Solution:

First, find the equivalent resistance: 1/R_eq = 1/4 + 1/8 = 3/8, so R_eq = 8/3Ω. Then, I = V/R_eq = 24V / (8/3)Ω = 9A.

In a circuit with a 24V battery and two resistors of 4Ω and 8Ω in parallel, what is the total current supplied by the battery? (2022)

In a circuit with a 24V battery and two resistors of 4Ω and 8Ω in parallel, what is the total current supplied by the battery? (2022)

Step 1: Identify the values given in the problem. We have a 24V battery and two resistors: one is 4Ω and the other is 8Ω.
Step 2: Since the resistors are in parallel, we need to find the equivalent resistance (R_eq).
Step 3: Use the formula for parallel resistors: 1/R_eq = 1/R1 + 1/R2. Here, R1 is 4Ω and R2 is 8Ω.
Step 4: Substitute the values into the formula: 1/R_eq = 1/4 + 1/8.
Step 5: Find a common denominator to add the fractions. The common denominator for 4 and 8 is 8.
Step 6: Rewrite the fractions: 1/4 = 2/8, so 1/R_eq = 2/8 + 1/8 = 3/8.
Step 7: Now, take the reciprocal to find R_eq: R_eq = 8/3Ω.
Step 8: Use Ohm's Law to find the total current (I) supplied by the battery. The formula is I = V/R_eq.
Step 9: Substitute the values: I = 24V / (8/3)Ω.
Step 10: Simplify the calculation: I = 24V * (3/8) = 9A.

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