In a parallel circuit with a 12V source and two resistors of 6Ω and 12Ω, what is

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Question: In a parallel circuit with a 12V source and two resistors of 6Ω and 12Ω, what is the total current drawn from the source?

Options:

Correct Answer: 3 A

Solution:

Total current I = V/R_total. R_total = 1/(1/6 + 1/12) = 4Ω. Thus, I = 12V / 4Ω = 3 A.

In a parallel circuit with a 12V source and two resistors of 6Ω and 12Ω, what is the total current drawn from the source?

In a parallel circuit with a 12V source and two resistors of 6Ω and 12Ω, what is the total current drawn from the source?

Step 1: Identify the voltage of the source, which is 12V.
Step 2: Identify the resistors in the circuit, which are 6Ω 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 / (1/6 + 1/12).
Step 5: Calculate 1/6 and 1/12: 1/6 = 0.1667 and 1/12 = 0.0833.
Step 6: Add these two values together: 0.1667 + 0.0833 = 0.25.
Step 7: Take the reciprocal of 0.25 to find R_total: R_total = 1 / 0.25 = 4Ω.
Step 8: Use Ohm's Law to find the total current (I) drawn from the source: I = V / R_total.
Step 9: Substitute the values: I = 12V / 4Ω.
Step 10: Calculate the total current: I = 3 A.

Parallel Circuits – In a parallel circuit, the voltage across each resistor is the same, and the total current is the sum of the currents through each resistor.
Equivalent Resistance – The equivalent resistance in a parallel circuit can be calculated using the formula 1/R_total = 1/R1 + 1/R2 + ... for all resistors.
Ohm's Law – Ohm's Law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R).