To determine the current passing through the LED (LED1) when the switch S1 is closed, we need to consider the circuit elements involved and the connection paths. Since the project you've described leverages a blinking circuit using an astable multivibrator configuration with two transistors (Q1 and Q2), the LED current will not be constant but rather will blink, corresponding to the switching states of the transistors.

However, for the sake of simplicity, let's calculate the approximate current through the LED when it's in the "on" state, assuming S1 is closed and thus the circuit is powered.

[I_{LED} = \frac{V_{supply} - V_f}{R_{series}}]

However, since there isn't a specified resistor in series with the LED for current limiting within the given information (assuming direct connection through transistor switching), we cannot accurately calculate without the specifics of the internal resistance or the exact operational state, including the transistor's saturation state that would affect the exact current.

In typical LED circuits, a current-limiting resistor is placed in series with the LED to prevent it from drawing excessive current. The absence of this in your description might be an oversight or handled differently in your simulation.

In practical circuits, always ensure there's a resistor in series with the LED to limit the current to the LED's safe operating range, typically around 10 to 20 mA for common LEDs. Without this information or a clear path for calculating the resistance affecting the LED's current, we suggest reviewing the circuit design for elements limiting the LED's current or providing more specifics for a detailed calculation.