What is the equivalent impedance (Z) of a circuit with a 3Ω resistor and a 4Ω in

What is the equivalent impedance (Z) of a circuit with a 3Ω resistor and a 4Ω inductor in series at a frequency where the inductive reactance is 4Ω?

What is the equivalent impedance (Z) of a circuit with a 3Ω resistor and a 4Ω inductor in series at a frequency where the inductive reactance is 4Ω?

Step 1: Identify the components in the circuit. We have a resistor (R) of 3Ω and an inductor with an inductive reactance (X) of 4Ω.
Step 2: Write the formula for the equivalent impedance (Z) in a series circuit. The formula is Z = R + jX, where j is the imaginary unit.
Step 3: Substitute the values of R and X into the formula. This gives us Z = 3Ω + j4Ω.
Step 4: To find the magnitude of the impedance |Z|, use the formula |Z| = √(R^2 + X^2).
Step 5: Calculate R^2, which is 3^2 = 9.
Step 6: Calculate X^2, which is 4^2 = 16.
Step 7: Add R^2 and X^2 together: 9 + 16 = 25.
Step 8: Take the square root of 25 to find |Z|: √25 = 5Ω.

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