A LCR circuit has $$L=10mH$$,$$R=3$$Ω, and $$C=1$$μF connected in series to a source of $$15cos$$⁡ωt volt . Calculate the current amplitude (in$$ $$ampere) at a frequency that is $$10$$ % lower than the resonant frequency.

Question

A LCR circuit has $$L=10mH$$,$$R=3$$Ω, and $$C=1$$μF connected in series to a source of $$15cos$$⁡ωt volt . Calculate the current amplitude (in$$ $$ampere) at a frequency that is $$10$$ % lower than the resonant frequency.

Infinity Learn · Accepted Answer

The resonance frequency, ​ω$$r=1LC=110$$×$$10$$−$$3$$×$$1$$×$$10$$−$$6$$​$$=104rad/s$$​Thus ,ω$$=0.90$$ω$$r=9$$×$$103rad/s$$​$$XL=$$ω$$L=9$$×$$103$$×(10$$×$$10$$−$$3)​$$=90$$Ω​and  $$XC=1$$ω$$C=19$$×$$103$$×$$10$$−$$6$$​$$=111.11$$Ω​The impedance, $$Z=R2+(XC-XL)2$$​$$=32+(111.11$$−$$90)2$$​$$=21.32$$Ω​ The current amplitude, ​$$i0=V0Z=1521.32=0.704A$$

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A LCR circuit has $L = 10 mH, R = 3 Ω, and C = 1 μ F$ connected in series to a source of $15 \cos ω t volt$ . Calculate the current amplitude (in ampere) at a frequency that is 10 % lower than the resonant frequency.

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A LCR circuit has L=10mH,R=3Ω, and C=1μF connected in series to a source of 15cos⁡ωt volt . Calculate the current amplitude (in ampere) at a frequency that is 10 % lower than the resonant frequency.

The resonance frequency, ​ωr=1LC=110×10−3×1×10−6​=104rad/s​Thus ,ω=0.90ωr=9×103rad/s​XL=ωL=9×103×(10×10−3)​=90Ω​and XC=1ωC=19×103×10−6​=111.11Ω​The impedance, Z=R2+(XC-XL)2​=32+(111.11−90)2​=21.32Ω​ The current amplitude, ​i0=V0Z=1521.32=0.704A

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A LCR circuit has $L = 10 mH, R = 3 Ω, and C = 1 μ F$ connected in series to a source of $15 \cos ω t volt$ . Calculate the current amplitude (in ampere) at a frequency that is 10 % lower than the resonant frequency.