What is the impedance of a circuit with a resistor of 10Ω and an inductor of 0.1

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Question: What is the impedance of a circuit with a resistor of 10Ω and an inductor of 0.1 H at a frequency of 50 Hz? (2022)

Options:

Correct Answer: 15.71Ω

Solution:

Impedance Z = √(R² + (XL)²), where XL = 2πfL = 31.42Ω. Thus, Z = √(10² + 31.42²) = 15.71Ω.

What is the impedance of a circuit with a resistor of 10Ω and an inductor of 0.1 H at a frequency of 50 Hz? (2022)

What is the impedance of a circuit with a resistor of 10Ω and an inductor of 0.1 H at a frequency of 50 Hz? (2022)

Step 1: Identify the values given in the problem. We have a resistor (R) of 10Ω and an inductor (L) of 0.1 H.
Step 2: Identify the frequency (f) given in the problem, which is 50 Hz.
Step 3: Calculate the inductive reactance (XL) using the formula XL = 2πfL.
Step 4: Substitute the values into the formula: XL = 2 * π * 50 * 0.1.
Step 5: Calculate XL: XL = 2 * 3.14 * 50 * 0.1 = 31.42Ω.
Step 6: Now, use the impedance formula Z = √(R² + (XL)²).
Step 7: Substitute R and XL into the formula: Z = √(10² + 31.42²).
Step 8: Calculate R²: 10² = 100.
Step 9: Calculate XL²: 31.42² = 987.0564.
Step 10: Add R² and XL²: 100 + 987.0564 = 1087.0564.
Step 11: Take the square root to find Z: Z = √(1087.0564) = 15.71Ω.

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