complex number(電路)

2012-12-26 7:37 am

For the RLC circuit shown in figure Q9,the supply voltage is v=220arg0 .The resistance of the resistor R is 15-ohm,the reactance XL of the inductor L is 20-ohm and the reactance XC of the capacitor C is 8-ohm.

┌──R────C────L───┐
│　　　　　　　　　　　　│
↑(I)　　　　　　　　　　　│
│　　　　　　　　　　　　│
│　　　　　　　　　　　　│
└───(V=220arg0)─────┘

Determine
1)the impedance Z of the circuit
2)the current I flowing in the circuit
3)the voltages across the resistor R,the inductor L and the capacitor C.
4)Sketch the voltages on the Argand diagram.

回答 (1)

用戶10012

2012-12-26 7:28 pm

✔ 最佳答案

1) Impedance = Resistance + Reactance.
Inductor is positive reactance and capacitor is negative reactance.
So impedance of circuit = 15 + 20j - 8j = 15 + 12j = 19.21 arg [arctan(12/15)]
= 19.21 arg 38.66
2)
Current = V/Z = 220 arg 0/19.21 arg 38.66 = 11.45 arg ( - 38.66)
3)
Voltage across resistor = IR = 15 x 11.45 arg ( - 38.66) = 171.79 arg ( - 38.66)
Voltage across inductor = IXL = 11.45 arg ( - 38.66) x 20 arg ( 90)
= 229 arg 51.34
Voltage across capacitor = IXC = 11.45 arg ( - 38.66) x 8 arg(- 90)
= 91.6 arg ( - 128.66)
4)
Vr = 134.14 - 107.32j
Vl = 143.06 + 178.82j
Vc = - 57.22 - 71.53j
Vr + Vl + Vc = 220 = supplied voltage.

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