Can anyone tell me what input impedance is?

[joker_900]

Homework Statement

Can anyone tell me what input impedance is?

The context is "...these two solenoids act as a transformer. An AC voltage Vexp[jwt] is placed across the first and a resistor R across the second. Show that the input impedance of the first solenoid is equivalent to a circuit consisting of an inductance L1 in parallel with a resistor R'. Find R'." L1 is the self-inductance of the first solenoid btw.

Homework Equations

The Attempt at a Solution

I thought the impedance of the first solenoid is just jwL, but apparently input impedance is different somehow?

 

[anathema]

Hello there, great question! Input impedance is a measure of the resistance that a circuit presents to a current that is being applied to it. In this case, the input impedance of the first solenoid in the transformer circuit would refer to the total resistance that the solenoid presents to the current coming from the AC voltage source. This includes both the inductive reactance (jwL1) and the resistance of the solenoid (R'). You are correct in thinking that the impedance of the first solenoid is jwL1, but to find the total input impedance, you would need to add R' to that value. This would give you the total impedance (Z) of the first solenoid, represented by the equation Z = R' + jwL1. I hope this helps clarify the concept of input impedance for you. Let me know if you have any further questions.

 

[Moetasim]

The input impedance of a circuit is a measure of how much the circuit resists the flow of current when a voltage is applied to it. It is the ratio of the voltage applied to the circuit to the resulting current. In the context of the given problem, the input impedance refers to the resistance that the first solenoid presents to the AC voltage source.

In this case, the input impedance is not just jwL, but a combination of inductance and resistance. This is because the solenoid has both inductance and resistance, which together determine the overall impedance of the circuit. The inductance L1 represents the reactance of the solenoid, while the resistor R represents the resistance.

To find the input impedance of the first solenoid, we can use the formula Z = √(R^2 + (jwL)^2), where Z is the input impedance, R is the resistance, and jwL is the reactance. This formula takes into account both the resistance and reactance of the solenoid, giving us a more accurate measure of the overall impedance.

In order to further simplify the circuit, we can also use the concept of parallel impedance. In this case, the input impedance of the first solenoid can be represented as the parallel combination of the inductance L1 and the resistor R. This can be calculated using the formula Z = (1/R + 1/(jwL))^-1.

Therefore, the input impedance of the first solenoid is not just jwL, but a combination of inductance and resistance. It is important to consider both of these factors in order to accurately calculate the input impedance and understand the behavior of the circuit.