Discussion

For the given circuit, find the collector current \(I_C\), if \(\beta = 100\) and \(V_{BE} = 0.7\) V.

Answer: B

Use the Thevenin equivalent of the base divider, with \(V_{CC} = 15\) V, \(R_1 = 6\ \text{k}\Omega\) and \(R_2 = 3\ \text{k}\Omega\).

\[ \begin{aligned} V_{TH} = 15 \times \frac{3}{6 + 3} \\ &= 5\ \text{V},\qquad R_{TH} = 6 \parallel 3 \\ &= 2\ \text{k}\Omega \end{aligned} \]

The base loop equation with \(I_E = (\beta + 1) I_B\) is

\[ 5 = I_B R_{TH} + 0.7 + (\beta + 1) I_B R_E \]

\[ \begin{aligned} I_B = \frac{4.3}{2 + 101 \times 1}\ \text{mA} \\ &= 0.0417\ \text{mA} \end{aligned} \]

\[ \begin{aligned} I_C = \beta I_B = 100 \times 0.0417 \\ &= 4.17 \approx 4.2\ \text{mA} \end{aligned} \]

The answer is 4.2 mA, option B. The other values are off by a factor of ten.

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