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 (assuming inductive reactance of 3Ω)?

Options:

Correct Answer: 13Ω

Solution:

Impedance Z = √(R^2 + X_L^2) = √(10^2 + 3^2) = √(100 + 9) = √109 ≈ 13Ω.

What is the impedance of a circuit with a 10Ω resistor and a 5Ω inductor at a frequency of 60Hz (assuming inductive reactance of 3Ω)?

What is the impedance of a circuit with a 10Ω resistor and a 5Ω inductor at a frequency of 60Hz (assuming inductive reactance of 3Ω)?

Step 1: Identify the resistance (R) of the circuit, which is given as 10Ω.
Step 2: Identify the inductive reactance (X_L) of the inductor, which is given as 3Ω.
Step 3: Use the formula for impedance (Z), which is Z = √(R^2 + X_L^2).
Step 4: Substitute the values into the formula: Z = √(10^2 + 3^2).
Step 5: Calculate R^2: 10^2 = 100.
Step 6: Calculate X_L^2: 3^2 = 9.
Step 7: Add the results from Step 5 and Step 6: 100 + 9 = 109.
Step 8: Take the square root of the sum: Z = √109.
Step 9: Calculate the square root: Z ≈ 13Ω.

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