An AC source powers a circuit containing a resistor, a capacitor, and an inductor as shown. L R C b a If the inductance is 1 H , the capacitance is 1 F , and the resistance 1 Ω , find the impedance Zab across a b . ω = 1.25 Hz and ω0 = 1 √ LC = 1 Hz . Answer in units of Ω.
Angular frequency, ω = 1.25 Hz
Frequency, f = ω / 2π
= 1.25 / 2π
= 0.199 Hz
Inductive reactance, XL = 2 π f L
= 2 π * 0.199 * 1
= 1.25 ohms
Capacitive reactance, XC = 1 / ( 2πf C )
= 1 / ( 2π * 0.199 * 1 )
= 0.80 ohms
Magnitude of impedance, z = √ [ R^2 + ( XL - XC )^2 ]
= √ [ 1^2 + ( 1.25 - 0.80 )^2 ]
= 1.1 Ω
An AC source powers a circuit containing a resistor, a capacitor, and an inductor as shown....
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