Question

find vb (assume a stiff bias circuit).
answer:

Explanation:

Step1: Calculate the total resistance of the voltage - dividing resistors

The two resistors in the voltage - dividing network are \(R_1 = 10\ \text{k}\Omega=10\times10^{3}\ \Omega\) and \(R_2 = 1.8\ \text{k}\Omega = 1.8\times 10^{3}\ \Omega\). The total resistance \(R_T=R_1 + R_2=(10 + 1.8)\times10^{3}\ \Omega=11.8\times10^{3}\ \Omega\)

Step2: Use the voltage - divider formula

The voltage - divider formula is \(V_B=\frac{R_2}{R_1 + R_2}\times V_{CC}\). Given \(V_{CC}=40\ \text{V}\), \(R_1 = 10\times10^{3}\ \Omega\), and \(R_2 = 1.8\times10^{3}\ \Omega\)

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In a stiff - bias circuit (also known as a voltage - divider bias circuit for a BJT), the base voltage \(V_B\) is determined by the voltage - divider formed by \(R_1\) and \(R_2\) connected to the supply voltage \(V_{CC}\). The assumption of a stiff - bias circuit implies that the base current \(I_B\) is small enough that it does not significantly affect the voltage - divider operation (i.e., \(I_{R1}\approx I_{R2}\)).

Answer:

\(6.55\ \text{V}\)