What is the Norton equivalent current (In) for a circuit with a 15V source and a

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Question: What is the Norton equivalent current (In) for a circuit with a 15V source and a 5Ω resistor in parallel with a 10Ω resistor?

Options:

Correct Answer: 2A

Solution:

In = V / R_parallel = 15V / (1/(1/5 + 1/10)) = 15V / (10/3) = 4.5A.

What is the Norton equivalent current (In) for a circuit with a 15V source and a 5Ω resistor in parallel with a 10Ω resistor?

What is the Norton equivalent current (In) for a circuit with a 15V source and a 5Ω resistor in parallel with a 10Ω resistor?

Step 1: Identify the voltage source in the circuit, which is 15V.
Step 2: Identify the resistors in parallel, which are 5Ω and 10Ω.
Step 3: Calculate the equivalent resistance (R_parallel) of the two resistors in parallel using the formula: 1/R_parallel = 1/R1 + 1/R2.
Step 4: Substitute the values of the resistors into the formula: 1/R_parallel = 1/5 + 1/10.
Step 5: Find a common denominator for the fractions, which is 10: 1/5 = 2/10, so 1/R_parallel = 2/10 + 1/10 = 3/10.
Step 6: Invert the fraction to find R_parallel: R_parallel = 10/3Ω.
Step 7: Use Ohm's law to find the Norton equivalent current (In) using the formula: In = V / R_parallel.
Step 8: Substitute the values into the formula: In = 15V / (10/3).
Step 9: Simplify the calculation: In = 15V * (3/10) = 45/10 = 4.5A.

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