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I am a student. Our teacher gave us a problem that can be done by Kirchhoff's laws. The problem is that in the second case we have to calculate β → ∞, the teachers told us to calculate β using a limit, but I don't know how to do this if there is no function to take the limit to ∞. This is the only information the problem gives. The (O1) and (O2) squares are loops from second Kirchhoff's law.
Rearranging the BJT forward active current gain:
$$I_c = βI_b $$ $$I_b = \frac{I_c}{β} $$ $$\lim_{β \to \infty} I_b = 0$$
Practically this means that for large β you can ignore the base current. In that case Ic = Ie, and you can find Ie using Ohm's law.
