Question #314308

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

If the resistance, inductance, and capacitance are all doubled, by what factor does each of the

following quantities change


1
Expert's answer
2022-03-21T12:46:53-0400

LCR series combination

Impedance

Z=R2+(XcXL)Z=\sqrt{R^2+(X_c-X_L)}

XL=XcX_L=X_c

Resonance frequency

wL=1wCwL=\frac{1}{wC}

w=1LCw=\frac{1}{\sqrt{LC}}

L=2L

C=2C

w=14LCw'=\frac{1}{\sqrt{4LC}}

ww=12\frac{w'}{w}=\frac{1}{2}

w=w2w'=\frac{w}{2}

Inductive reactance

XL=wLX_L=wL

XL=2wLL=2LX'_L={2wL}\\L'=2L

XLXL=2wLwL\frac{X'_L}{X_L}=\frac{2w_L}{wL}

XL=2XLX'_L=2X_L

Capacitive reactance

Xc=1wCX_c=\frac{1}{wC}

C'=2C

Xc=12wCX'_c=\frac{1}{2wC}

XcXc=12\frac{X'_c}{X_c}=\frac{1}{2}

XC=Xc2X'_C=\frac{X_c}{2}


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