Determine the range of possible values for VC for the network of Fig. 4.132 using the 1-MΩ...

Determine the collector current \(I_{C}\).

$$ \begin{aligned} I_{C} &=\beta I_{B} \\ &=180\left(7.11 \times 10^{-6}\right) \\ &=1.28 \mathrm{~mA} \end{aligned} $$

Use Kirchhoff's voltage law to write the expression for the collector voltage \(V_{C}\).

\(V_{C}=V_{C C}-I_{C} R_{C}\)

Substitute \(1.28 \mathrm{~mA}\) for \(I_{C}, 4.7 \mathrm{k} \Omega\) for \(R_{C}\) and \(12 \mathrm{~V}\) for \(V_{C C}\)

$$ \begin{aligned} V_{C} &=12-\left(1.28 \times 10^{-3}\right)\left(4.7 \times 10^{3}\right) \\ &=12-6.02 \\ &=5.98 \mathrm{~V} \end{aligned} $$

Consider the resistance of the potentiometer is \(1 \mathrm{M} \Omega\).

The equivalent resistance at the base terminal of the transistor is,

$$ \begin{aligned} R_{B} &=150 \mathrm{k} \Omega+1 \mathrm{M} \Omega \\ &=150 \mathrm{k} \Omega+1000 \mathrm{k} \Omega \\ &=1150 \mathrm{k} \Omega \end{aligned} $$

Write the expression for the base current \(I_{B}\).

$$ I_{B}=\frac{V_{C C}-V_{B E}}{R_{B}+\beta\left(R_{C}+R_{E}\right)} $$

Substitute \(1150 \mathrm{k} \Omega\) for \(R_{B}, 4.7 \mathrm{k} \Omega\) for \(R_{C}, 3.3 \mathrm{k} \Omega\) for \(R_{E}, 180\) for \(\beta, 12 \mathrm{~V}\) for \(V_{C C}\) and

$$ \begin{aligned} &0.7 \mathrm{~V} \text { for } V_{B E} . \\ &\qquad \begin{aligned} I_{B} &=\frac{12-0.7}{1150 \times 10^{3}+180\left(4.7 \times 10^{3}+3.3 \times 10^{3}\right)} \\ &=\frac{11.3}{1150 \times 10^{3}+1440 \times 10^{3}} \\ &=\frac{11.3}{2590 \times 10^{3}} \\ &=4.363 \mu \mathrm{A} \end{aligned} \end{aligned} $$

Determine the collector current \(I_{C}\).

$$ \begin{aligned} I_{C} &=\beta I_{B} \\ &=180\left(4.363 \times 10^{-6}\right) \\ &=0.78 \mathrm{~mA} \end{aligned} $$

Use Kirchhoff's voltage law to write the expression for the collector voltage \(V_{C}\).

\(V_{C}=V_{C C}-I_{C} R_{C}\)

Substitute \(0.78 \mathrm{~mA}\) for \(I_{C}, 4.7 \mathrm{k} \Omega\) for \(R_{C}\) and \(12 \mathrm{~V}\) for \(V_{C C}\).

$$ \begin{aligned} V_{C} &=12-\left(0.78 \times 10^{-3}\right)\left(4.7 \times 10^{3}\right) \\ &=12-3.69 \\ &=8.31 \mathrm{~V} \end{aligned} $$

Thus, the range of \(V_{C}\) is \(5.98 \mathrm{~V}\) to \(8.31 \mathrm{~V}\).