In a parallel circuit with a 12V battery and two resistors (4Ω and 12Ω), what is

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Question: In a parallel circuit with a 12V battery and two resistors (4Ω and 12Ω), what is the total current supplied by the battery?

Options:

Correct Answer: 3 A

Solution:

Total current I = V/R_total. R_total = 1/(1/4 + 1/12) = 3Ω. I = 12V / 3Ω = 4 A.

In a parallel circuit with a 12V battery and two resistors (4Ω and 12Ω), what is the total current supplied by the battery?

In a parallel circuit with a 12V battery and two resistors (4Ω and 12Ω), what is the total current supplied by the battery?

Step 1: Identify the voltage of the battery, which is 12V.
Step 2: Identify the resistors in the circuit, which are 4Ω and 12Ω.
Step 3: Calculate the total resistance (R_total) for the parallel circuit using the formula: R_total = 1 / (1/R1 + 1/R2).
Step 4: Substitute the values of the resistors into the formula: R_total = 1 / (1/4 + 1/12).
Step 5: Find a common denominator for the fractions: The common denominator for 4 and 12 is 12.
Step 6: Rewrite the fractions: 1/4 = 3/12 and 1/12 = 1/12.
Step 7: Add the fractions: 1/4 + 1/12 = 3/12 + 1/12 = 4/12.
Step 8: Take the reciprocal to find R_total: R_total = 1 / (4/12) = 12/4 = 3Ω.
Step 9: Use Ohm's Law to find the total current (I) supplied by the battery: I = V / R_total.
Step 10: Substitute the values: I = 12V / 3Ω.
Step 11: Calculate the total current: I = 4 A.

Ohm's Law – The relationship between voltage (V), current (I), and resistance (R) in an electrical circuit, expressed as I = V/R.
Parallel Circuit Rules – In a parallel circuit, the total resistance (R_total) is found using the formula 1/R_total = 1/R1 + 1/R2 + ... for all resistors in parallel.