Parallel RLC circuit diagram - application of complex numbers


For Z1 (the upper part of the circuit), we have:

XL = 2πfL = 2π (60)(0.0200) ` `= 7.540 Ω

`X_C=1/(2pi(60)(1.20xx10^-6))` `=2210.485\ Omega`

Z1 = R1 + j(XLXC)

= 100 + j(7.540 - 2210.485)

= 100 − 2202.9j

`= 2205.21 ∠ − 87.40^@\ Ω`

For Z2 (the lower part of the circuit), we have:

`X_C=1/(2pi(60)(2.40xx10^-6))` `=1105.243\ Omega`

Z2 = R2 + j(XL - XC)

= 110 + j(−1105.243)

`= 1110.7 ∠ −84.32^@\ Ω`

So the total impedance, ZT, is given by:

`Z_T=(Z_1Z_2)/(Z_1+Z_2)`

`=(2449326.75/_-171.72^"o")/(210-3308.188j)`

`=(2449326.75/_-171.72^"o")/(3314.85/_-86.37^"o")`

`=738.9/_-85.35^"o"`

This last line in rectangular form is ZT = 59.9 − 736.5j Ω

Now:

`I_T=(V_T)/(Z_T)`

`=(150/_0^"o")/(738.9/_-85.35^"o")`

`=0.203/_85.35^"o"`

So the total current taken from the supply is `203\ "mA"` and the phase angle of the current is `~~85^@`.

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