Question

At the pure inductive stage, find e_max.

Answer 1

At the pure inductive stage, the maximum voltage or e_max can be determined by the equation: 

e_max = I_max \(\times\) X_L 

where I_max is the maximum current flowing through the inductor and X_L is the inductive reactance. 

Inductive reactance (X_L) is calculated using the formula: 

X_L = 2πf_L 

where f is the frequency of the alternating current (AC) signal and L is the inductance of the inductor. 

To find e_max, you would need to know the values of Imax, f, and L for the specific circuit or scenario in question. Once you have those values, you can substitute them into the equations to calculate the maximum voltage or e_max at the pure inductive stage.

Answer 2

In an ideal pure inductive circuit, the maximum emf (\(e_{\text{max}}\)) occurs when the rate of change of current (\(\frac{di}{dt}\)) is maximum. This happens when the circuit is first connected to a voltage source or when the voltage across the inductor changes abruptly.
Key Points for Pure Inductive Circuit:
1. Inductor Behavior: In a pure inductive circuit, the voltage across the inductor \(V_L\) depends on the rate of change of current through it, given by \( V_L = L \frac{di}{dt} \), where \( L \) is the inductance.
2. Maximum emf (\( e_{\text{max}} \)): This occurs when the current through the inductor changes most rapidly, such as when the circuit is first energized or de-energized.
Mathematical Explanation:
When the switch in an inductive circuit is closed or opened, the current through the inductor changes abruptly. At this moment, the inductor opposes this change by inducing a voltage (emf) to maintain current continuity. The magnitude of this emf \( e_{\text{max}} \) can be quite large, theoretically infinite in an ideal case with zero resistance.
 Conclusion:
- Maximum emf (\( e_{\text{max}} \)): The maximum emf in a pure inductive circuit occurs at the moment when the current change (\(\frac{di}{dt}\)) is maximum, typically when the circuit is first connected or disconnected.
- The exact numerical value of \( e_{\text{max}} \) would depend on the specific circuit parameters such as inductance \( L \) and the rate of change of current (\(\frac{di}{dt}\)), but in theoretical terms, it can be very high.