## Analyzing a Series RLC Circuit A series RLC circuit has R-420 Ω, L = 1.10 H, C = 3.6 μF. It is connected to an AC source with f= 60.0 Hz and ΔⅤmax = 150 V. SOLVE IT (A) Determine the inductive reactance, the capacitive reactance, and the impedance of the circuit. Conceptualize: The circuit of interest in this example is shown in the figure. The current in the combination of the resistor, inductor, and capacitor oscillates at a particular phase angle with respect to the applied voltage. A series circuit consisting of a resistor, an inductor, and a capacitor connected to an AC source Categorize: The circuit is a simple series RLC circuit, so we can use the approach discussed in this section. Analyze: Find the angular frequency: a) = 2㎡=2r(60.0 Hz) = 376.99 rad/s (377 rad/s)(1.10 H) Use the following equation to find the inductive reactance: XL = ω 414.7 1 Use the following equation to find the capacitive reactance: wC (377 rad/s)(3.60 x 106 F) Ω X-= 736.811 Z = V R2 + (XL-XC) Use the following equation to find the impedance: 2 z-V (420 Ω)2 + (414.48 Ω-737.20 Ω)2 Z= 529.67

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