Find the capacitance C1 such that module of complex current through the R is maximal. Known values are:
R1=20Ω, R3=3Ω, L1=8mH, L2=4mH,C3=259uF, ω=10^3 rad/s k=sqrt(2)/2
Circuit:
This is how i solved it:
Since i have to find the current through the R, that means it's the same current as current through C1, so i could leave C1 and E alone, and find equivalent impedance for the rest of the circuit. If i choose the direction of currents such that both currents in branches with inductors are going 'in' the points since k is positive, so, basically i have a circuit with L1, L12 and R in series, and L2 + L12 in parallel with C3 and R3.
Since i know k i can find L12 and its L12=4mH. S impedance Z1= jωL1 + jωL12 + R and Z3=R3 - j/ωC and Z2=jωL2 + jωL12 so Ze=Z1 + (Z2||Z3) .
When i compute all of this i get Ze=(22.7 + j12.75)Ω.
So now i have a circuit with E, C and Ze so current
I1=E/(22.7 + j12.75 + 1/jωc)
I1=E/(22.7 + j12.75 - j/ωc)
I1=E/(22.7 + j(12.75 - 1/ωc))
Current will be greatest if denominator is lowest possible, and when looking at C, it will be lowest if 1/ωC=12.75
which means that C=78.4 uC.
Is this valid approach, and is this correct?
R1=20Ω, R3=3Ω, L1=8mH, L2=4mH,C3=259uF, ω=10^3 rad/s k=sqrt(2)/2
Circuit:
This is how i solved it:
Since i have to find the current through the R, that means it's the same current as current through C1, so i could leave C1 and E alone, and find equivalent impedance for the rest of the circuit. If i choose the direction of currents such that both currents in branches with inductors are going 'in' the points since k is positive, so, basically i have a circuit with L1, L12 and R in series, and L2 + L12 in parallel with C3 and R3.
Since i know k i can find L12 and its L12=4mH. S impedance Z1= jωL1 + jωL12 + R and Z3=R3 - j/ωC and Z2=jωL2 + jωL12 so Ze=Z1 + (Z2||Z3) .
When i compute all of this i get Ze=(22.7 + j12.75)Ω.
So now i have a circuit with E, C and Ze so current
I1=E/(22.7 + j12.75 + 1/jωc)
I1=E/(22.7 + j12.75 - j/ωc)
I1=E/(22.7 + j(12.75 - 1/ωc))
Current will be greatest if denominator is lowest possible, and when looking at C, it will be lowest if 1/ωC=12.75
which means that C=78.4 uC.
Is this valid approach, and is this correct?