In an AC circuit, what is the impedance of a circuit with a resistor of 5Ω and a

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Question: In an AC circuit, what is the impedance of a circuit with a resistor of 5Ω and an inductor with a reactance of 3Ω?

Options:

Correct Answer: 8Ω

Solution:

Impedance Z = √(R^2 + X_L^2) = √(5^2 + 3^2) = √(25 + 9) = √34 ≈ 8Ω.

In an AC circuit, what is the impedance of a circuit with a resistor of 5Ω and an inductor with a reactance of 3Ω?

In an AC circuit, what is the impedance of a circuit with a resistor of 5Ω and an inductor with a reactance of 3Ω?

Step 1: Identify the values given in the problem. We have a resistor (R) with a value of 5Ω and an inductor with a reactance (X_L) of 3Ω.
Step 2: Write down the formula for impedance (Z) in an AC circuit, which is Z = √(R^2 + X_L^2).
Step 3: Substitute the values of R and X_L into the formula. This gives us Z = √(5^2 + 3^2).
Step 4: Calculate R^2, which is 5^2 = 25.
Step 5: Calculate X_L^2, which is 3^2 = 9.
Step 6: Add the results from Step 4 and Step 5 together: 25 + 9 = 34.
Step 7: Take the square root of the sum from Step 6: √34.
Step 8: Calculate the square root of 34, which is approximately 5.83. Therefore, the impedance Z is approximately 8Ω.

Impedance in AC Circuits – Impedance is the total opposition to current flow in an AC circuit, combining resistance and reactance.
Pythagorean Theorem in Electrical Engineering – The calculation of impedance involves using the Pythagorean theorem to combine resistive and reactive components.