What is the impedance of a series R-L-C circuit at angular frequency ω?

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Multiple Choice

What is the impedance of a series R-L-C circuit at angular frequency ω?

Explanation:
In a series R-L-C circuit, impedances simply add. The resistor contributes a real part R. The inductor adds an imaginary part jωL. The capacitor contributes 1/(jωC), which simplifies to -j/(ωC) because 1/(j) = -j. Put together, the total impedance is Z = R + jωL - j/(ωC) = R + j(ωL − 1/(ωC)). The imaginary part, ωL − 1/(ωC), is the net reactance and can be positive (net inductive) or negative (net capacitive); at ω0 = 1/√(LC) the reactances cancel and Z = R.

In a series R-L-C circuit, impedances simply add. The resistor contributes a real part R. The inductor adds an imaginary part jωL. The capacitor contributes 1/(jωC), which simplifies to -j/(ωC) because 1/(j) = -j. Put together, the total impedance is Z = R + jωL - j/(ωC) = R + j(ωL − 1/(ωC)). The imaginary part, ωL − 1/(ωC), is the net reactance and can be positive (net inductive) or negative (net capacitive); at ω0 = 1/√(LC) the reactances cancel and Z = R.

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