What is the total impedance of a series circuit with a resistor of 4 ohms and an

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Question: What is the total impedance of a series circuit with a resistor of 4 ohms and an inductor with a reactance of 3 ohms?

Options:

Correct Answer: 7 ohms

Solution:

In a series circuit, total impedance Z = R + jX, so Z = 4 + j3, which has a magnitude of 7 ohms.

What is the total impedance of a series circuit with a resistor of 4 ohms and an inductor with a reactance of 3 ohms?

What is the total impedance of a series circuit with a resistor of 4 ohms and an inductor with a reactance of 3 ohms?

Step 1: Identify the values given in the problem. We have a resistor (R) of 4 ohms and an inductor with a reactance (X) of 3 ohms.
Step 2: Understand that in a series circuit, the total impedance (Z) is calculated using the formula Z = R + jX, where j represents the imaginary unit.
Step 3: Substitute the values into the formula: Z = 4 + j3.
Step 4: To find the magnitude of the total impedance, use the formula |Z| = √(R^2 + X^2).
Step 5: Calculate R^2: 4^2 = 16.
Step 6: Calculate X^2: 3^2 = 9.
Step 7: Add R^2 and X^2: 16 + 9 = 25.
Step 8: Take the square root of the sum: √25 = 5.
Step 9: The total impedance Z is 4 + j3, and its magnitude is 5 ohms.

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