Introduction:
In an R-L circuit connected to an alternating sinusoidal voltage, the transient current refers to the initial current that flows through the circuit when it is first closed. This transient current occurs before the system reaches its steady-state behavior. The size of this transient current primarily depends on the instant in the voltage cycle at which the circuit is closed.

Explanation:
When an R-L circuit is connected to an alternating sinusoidal voltage, the voltage across the circuit undergoes continuous changes over time. This sinusoidal voltage can be represented by a waveform that oscillates between positive and negative peaks. The transient current occurs during the initial phase of the circuit when the voltage is changing.

Effect of instant in the voltage cycle:
The instant in the voltage cycle at which the circuit is closed plays a crucial role in determining the size of the transient current. This is because the voltage waveform is not static, and its value at a specific instant determines the instantaneous current flow.

Explanation with examples:
1. If the circuit is closed at the peak of the positive half-cycle of the voltage waveform, the voltage is at its maximum value. At this instant, the rate of change of voltage is zero, resulting in a smaller transient current. This is because the inductor opposes changes in current, and when the voltage is at its maximum, the inductor tends to resist any further increase in current.

2. On the other hand, if the circuit is closed at the zero-crossing point of the voltage waveform, the rate of change of voltage is maximum. In this case, the inductor has a maximum opposition to the change in current, resulting in a larger transient current.

Conclusion:
Therefore, the instant in the voltage cycle at which the circuit is closed determines the magnitude of the transient current in an R-L circuit connected to an alternating sinusoidal voltage. Closing the circuit at the peak of the positive half-cycle results in a smaller transient current, while closing it at the zero-crossing point leads to a larger transient current. It is important to consider this factor when analyzing the behavior of R-L circuits in transient conditions.