What is the impedance of a circuit with a 10Ω resistor and a 5Ω inductor at a fr

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Question: What is the impedance of a circuit with a 10Ω resistor and a 5Ω inductor at a frequency of 60Hz?

Options:

Correct Answer: 12.25Ω

Solution:

Impedance Z = √(R^2 + (XL)^2), where XL = 2πfL. Assuming L = 5Ω, Z = √(10^2 + (2π*60*5)^2) = 12.25Ω.

What is the impedance of a circuit with a 10Ω resistor and a 5Ω inductor at a frequency of 60Hz?

What is the impedance of a circuit with a 10Ω resistor and a 5Ω inductor at a frequency of 60Hz?

Step 1: Identify the values given in the problem. We have a resistor (R) of 10Ω and an inductor (L) of 5Ω at a frequency (f) of 60Hz.
Step 2: Calculate the inductive reactance (XL) using the formula XL = 2πfL. Substitute the values: XL = 2 * π * 60 * 5.
Step 3: Calculate the value of XL. First, calculate 2 * π (approximately 6.2832), then multiply by 60 and 5 to get XL.
Step 4: Now, use the formula for impedance (Z): Z = √(R^2 + (XL)^2). Substitute R = 10Ω and the calculated XL value.
Step 5: Calculate R^2, which is 10^2 = 100. Then calculate (XL)^2 using the value from Step 3.
Step 6: Add R^2 and (XL)^2 together.
Step 7: Take the square root of the sum from Step 6 to find the impedance Z.

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