What is the impedance of a circuit with a 4Ω resistor and a 3Ω inductor at a fre

What is the impedance of a circuit with a 4Ω resistor and a 3Ω inductor at a frequency of 60Hz?

What is the impedance of a circuit with a 4Ω resistor and a 3Ω inductor at a frequency of 60Hz?

Step 1: Identify the values given in the problem. We have a resistor (R) of 4Ω and an inductor (L) of 3Ω at a frequency (f) of 60Hz.
Step 2: Calculate the inductive reactance (X_L) using the formula X_L = 2πfL. Here, f = 60Hz and L = 3Ω.
Step 3: Substitute the values into the formula: X_L = 2 * π * 60 * 3.
Step 4: Calculate the value of X_L. First, calculate 2 * π * 60, which is approximately 376.99. Then multiply by 3 to get X_L ≈ 1130.97Ω.
Step 5: Now, use the impedance formula Z = √(R^2 + (X_L)^2). Substitute R = 4Ω and X_L = 1130.97Ω.
Step 6: Calculate R^2, which is 4^2 = 16. Then calculate (X_L)^2, which is (1130.97)^2 ≈ 1280000.
Step 7: Add R^2 and (X_L)^2 together: 16 + 1280000 = 1280016.
Step 8: Take the square root of the sum to find Z: Z = √(1280016) ≈ 1131Ω.

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