• Tusike
In summary, the conversation discusses a parallel circuit on 230V, 60Hz voltage with a 0.0768H coil and 50 Ohm resistance. The question is about calculating the effective current in the main circuit. Two methods are suggested, but one is incorrect due to not considering complex impedances. The correct method involves calculating the magnitude of the reciprocal resultant impedance.
Tusike

## Homework Statement

Hi!
We have a parallel circuit on 230V, 60Hz voltage. One of the parallel's has a 0.0768H coil, the other has a 50 Ohm resistance on it. The question is: What is the effective I in the main current?

Z = Lw

## The Attempt at a Solution

OK, so I have two ways of solving this, and they lead to different results, I don't know which isn't correct and why.

#1). The impedance of the resistance is the same, 50 Ohms, while the impedance of the coil is L*w = 0.0768H * 120*pi = 28.868 Ohms. And so for the overall impedance: 1/Z = 1/Z(R) + 1/Z(L) = 1/50 + 1/28.868 = 0.05464 and so Z = 18.3 Ohms. For the effective I in the main current; I(eff) = U/Z = 230V/18.3Ohms = 12.567A.

#2) Since the coil's current is 90 degrees behind the resistance's, it is true that the main current i^2 = i(ZL)^2 + i(ZR)^2, where i(ZL) is the current in the coil and i(ZR) is the current in the resistance at a given point in time. Divide this equation by sqr(2)*sqr(2) to get the same equation for the effective currents: I^2 = I(ZL)^2 + I(ZR)^2.
We have calculated before that Z(L) = 28.868, so I(ZL) = 230/28.868=7.9673A. Z(R) = R = 50, so I(ZR) = 230 / 50 = 4.6A. And so the effective current in the main current is sqr(7.9672^2 + 4.6^2) = 9.2A.

Can anybody please tell me what I did wrong and why is it wrong? Thanks!

-Tusike

Tusike said:

## Homework Equations

Z = Lw

#1). The impedance of the resistance is the same, 50 Ohms, while the impedance of the coil is L*w = 0.0768H * 120*pi = 28.868 Ohms. And so for the overall impedance: 1/Z = 1/Z(R) + 1/Z(L) = 1/50 + 1/28.868 = 0.05464 and so Z = 18.3 Ohms.

You can not simply add up impedances or reciprocal impedances. If you learned about complex impedances, you should handle them as complex numbers. ZL=iwL where i is the imaginary unit. So the reciprocal resultant impedance is 1/Z=1/(iwL)+1/R = 1/R-i/wL. The magnitude is obtained as |1/Z|=sqrt((1/wL)2+(1/R)2), |Z|= 25 ohm

Last edited:
Oh OK I see now. I didn't learn yet about calculating with imaginary numbers, so for now I'll just use my other method, but I'll definitely look into this after I'm finished.

Thanks!

## 1. What is impedance paradox?

Impedance paradox is a phenomenon in electrical engineering where a circuit with a high impedance value can still allow a high current to flow through it. This is contrary to the traditional understanding that a high impedance circuit should restrict the flow of current.

## 2. What causes impedance paradox?

The impedance paradox is caused by the presence of a strong source of electromotive force (EMF) in the circuit. This EMF can overcome the resistance offered by the high impedance circuit, allowing a larger current to flow through it.

## 3. How is impedance paradox measured?

The impedance paradox is measured by calculating the ratio of voltage to current in the circuit. A high voltage-to-current ratio indicates a high impedance value, while a low ratio indicates a low impedance value.

## 4. What are the implications of impedance paradox?

The implications of impedance paradox include difficulties in designing and analyzing circuits, as well as potential safety hazards. It is important for engineers to understand and account for this phenomenon in order to ensure the proper functioning and safety of electrical systems.

## 5. Can impedance paradox be avoided?

Impedance paradox cannot be completely avoided, as it is a natural occurrence in electrical circuits. However, it can be minimized by using components with consistent and predictable impedance values, and by carefully considering the effects of EMF in circuit design.

Replies
3
Views
4K
Replies
4
Views
635
Replies
7
Views
829
Replies
2
Views
1K
Replies
1
Views
1K
Replies
5
Views
2K
Replies
13
Views
2K
Replies
5
Views
1K
Replies
9
Views
2K
Replies
30
Views
4K