An inductor, a capacitor, and a resistor are all connected in series across an a

Question

An inductor, a capacitor, and a resistor are all connected in series across an ac source. If the resistance, inductance, and capacitance are all quadrupled, by what factor does each of the following quantities change? Indicate whether they increase or decrease. (Let the size of your answer indicate whether it is a decrease or increase in the quantity.)     (a) the resonance angular frequency
1          

    (b) the inductive reactance
2

    (c) the capacitive reactance
3               (a) the resonance angular frequency
1          

    (b) the inductive reactance
2

    (c) the capacitive reactance
3          

Explanation / Answer

a) resonance frequency

Lw' = 1/Cw'

w' = 1/sqrt(LC)

w' = 1/sqrt(4L*4C)

w' = (1/4)*w

w' = 0.25 w (decrease)

b) inductive reactance Xl = Lw

Xl' = L'w'

Xl' = 4L* w

Xl' = 4*Xl (increase)

so Xl' is 4 times Xl

c) capacitive reactance Xc = 1/Cw

Xc' = 1/C'w'

Xc' = 1/4C*w

Xc' = 0.25*Xc (decrease)

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