What is the impedance of a series circuit containing a resistor (R) and an induc

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Question: What is the impedance of a series circuit containing a resistor (R) and an inductor (L) at angular frequency ω? (2020)

Options:

Correct Answer: √(R² + (ωL)²)

Exam Year: 2020

Solution:

The impedance Z in a series R-L circuit is given by Z = √(R² + (ωL)²).

What is the impedance of a series circuit containing a resistor (R) and an inductor (L) at angular frequency ω? (2020)

What is the impedance of a series circuit containing a resistor (R) and an inductor (L) at angular frequency ω? (2020)

Step 1: Understand that impedance (Z) is a measure of how much a circuit resists the flow of electric current.
Step 2: Identify the components in the circuit: a resistor (R) and an inductor (L).
Step 3: Recognize that the inductor's reactance (opposition to current) depends on the angular frequency (ω) and is given by the formula: X_L = ωL.
Step 4: Calculate the total impedance (Z) in a series circuit using the formula: Z = √(R² + (X_L)²).
Step 5: Substitute X_L with ωL in the formula: Z = √(R² + (ωL)²).
Step 6: This final formula Z = √(R² + (ωL)²) gives you the impedance of the series R-L circuit.

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