An ideal automotive battery has an open circuit voltage [tex]$V_{oc} = 13.5 \, \text{V}$[/tex] and a short circuit current [tex]$I_{sc} = 900 \, \text{A}$[/tex].

1. Determine the battery's Thevenin Equivalent resistance [tex]R_t[/tex].
2. Determine the maximum average power that this circuit can deliver to a resistive load.

The battery's Thevenin Equivalent resistance (Rt) is 0.015 Ω. The maximum average power that this circuit can deliver to a resistive load is 607.5 W.

Explanation:

To determine the battery's Thevenin Equivalent resistance (Rt), we can use the formula:

Rt = Voc / Isc

Substituting the given values:

Rt = 13.5 V / 900 A

Rt = 0.015 Ω

Therefore, the battery's Thevenin Equivalent resistance (Rt) is 0.015 Ω.

To determine the maximum average power that this circuit can deliver to a resistive load, we need to find the load resistance (Rload) that maximizes the power transfer. According to the maximum average power transfer theorem, the load resistance should be equal to the Thevenin Equivalent resistance (Rt) of the source.

Therefore, the maximum average power that this circuit can deliver to a resistive load is:

Pmax = (Voc^2) / (4 * Rt)

Substituting the given values:

Pmax = (13.5 V)^2 / (4 * 0.015 Ω)

Pmax = 607.5 W

Therefore, the maximum average power that this circuit can deliver to a resistive load is 607.5 W.

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