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fayled
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Given a series LCR circuit with a driving voltage V=V0cos(ωt), would it be possible to obtain a solution for I(t) by the two methods listed below?
1. Summing the voltages, i.e LdI/dt+IR+Q/C=V0cos(ωt) and solving the DE.
2. Using I=V/Z where Z is the total complex impedance and solving for I in terms of known values.
I ask this because this is something I have been trying to do. However I keep obtaining different solutions for the phase (although quite similar) which are
tanø=Rω/(-Lω2+1/C) using method 1. and tanø=(ωL-1/ωC/R) by method 2. with the current lagging the voltage in each case by ø.
I will be able to post further working if it is possible but I thought writing it all down now may be a waste of time if the method is flawed. Thanks.
1. Summing the voltages, i.e LdI/dt+IR+Q/C=V0cos(ωt) and solving the DE.
2. Using I=V/Z where Z is the total complex impedance and solving for I in terms of known values.
I ask this because this is something I have been trying to do. However I keep obtaining different solutions for the phase (although quite similar) which are
tanø=Rω/(-Lω2+1/C) using method 1. and tanø=(ωL-1/ωC/R) by method 2. with the current lagging the voltage in each case by ø.
I will be able to post further working if it is possible but I thought writing it all down now may be a waste of time if the method is flawed. Thanks.