What is the impedance (Z) of a circuit with a 4Ω resistor and a 3Ω inductor at a

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Question: What is the impedance (Z) of a circuit with a 4Ω resistor and a 3Ω inductor at a frequency where the inductive reactance (XL) is 3Ω?

Options:

Correct Answer: 5Ω

Solution:

Z = √(R² + XL²) = √(4² + 3²) = √(16 + 9) = √25 = 5Ω.

What is the impedance (Z) of a circuit with a 4Ω resistor and a 3Ω inductor at a frequency where the inductive reactance (XL) is 3Ω?

What is the impedance (Z) of a circuit with a 4Ω resistor and a 3Ω inductor at a frequency where the inductive reactance (XL) is 3Ω?

Step 1: Identify the values given in the problem. We have a resistor (R) of 4Ω and an inductor with an inductive reactance (XL) of 3Ω.
Step 2: Write down the formula for impedance (Z) in a circuit with a resistor and an inductor. The formula is Z = √(R² + XL²).
Step 3: Substitute the values of R and XL into the formula. This gives us Z = √(4² + 3²).
Step 4: Calculate R². 4² = 16.
Step 5: Calculate XL². 3² = 9.
Step 6: Add the results from Step 4 and Step 5. 16 + 9 = 25.
Step 7: Take the square root of the sum from Step 6. √25 = 5.
Step 8: State the final answer. The impedance (Z) of the circuit is 5Ω.

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