complex number(電路)

用戶81554

2012-12-24 9:23 am

An electrical circuit has a 40-ohm resistor in series with a 50-ohm coil.A 50 Hz,
240V supply is applied across the circuit.

1)Find the impedance of the circuit in rectangular form.
2)Express the impedance in polar form.
3)Find the current flowing.
4)Find the voltage across the resistor and the coil.

回答 (1)

用戶10012

2012-12-24 3:54 pm

✔ 最佳答案

Assume the coil is 50mH, not 50 ohm.
jwL = j (2pf)L = j [2 x 3.1416 x 50 x 50 x 10^(-3)] = 15.708j
1) Impedance, Z = 50 + 15.708j
2) In polar form is sqrt(50^2 + 15.708^2) arg ( arctan 15.708/50)
= 52.409 arg ( 17.44)
3) Voltage = 240 arg (0)
So current, I = V/Z = 240/52.409 arg(0 - 17.44) = 4.58 arg ( - 17.44)
4)
Voltage across the resistor = IR = (4.58)(50)arg(0 -17.44) = 229 arg ( - 17.44)
Impedance of coil in polar form = 15.708 arg ( 90)
So voltage across the coil = IZ = (4.58)(15.708) arg ( 90 - 17.44)
= 71.9 arg ( 72.56)

2012-12-24 08:01:13 補充：
Note : If impedance of the coil is really 50 ohm, then impedance of the circuit will simply be 50 + 50j = 70.71 arg ( 45). The frequency of 50Hz is then not necessary. Other calculation is the same.

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