1. **Problem Statement:** Determine the voltage $V_{CB}$ in the given silicon transistor circuit with $\beta = 150$, $R_C = 100\ \Omega$, $R_B = 10\ \text{k}\Omega$, $V_{CC} = 10\ \text{V}$, and $V_{BB} = 5\ \text{V}$. 2. **Known Parameters and Assumptions:** - Silicon transistor base-emitter voltage drop $V_{BE} \approx 0.7\ \text{V}$. - $\beta$ (current gain) = 150. 3. **Step 1: Calculate base current $I_B$** Using the base loop: $$V_{BB} = I_B R_B + V_{BE}$$ Rearranged: $$I_B = \frac{V_{BB} - V_{BE}}{R_B} = \frac{5 - 0.7}{10,000} = \frac{4.3}{10,000} = 0.00043\ \text{A} = 0.43\ \text{mA}$$ 4. **Step 2: Calculate collector current $I_C$** $$I_C = \beta I_B = 150 \times 0.00043 = 0.0645\ \text{A} = 64.5\ \text{mA}$$ 5. **Step 3: Calculate collector voltage $V_C$** Using the collector loop: $$V_C = V_{CC} - I_C R_C = 10 - (0.0645)(100) = 10 - 6.45 = 3.55\ \text{V}$$ 6. **Step 4: Calculate base voltage $V_B$** $$V_B = V_{BB} - I_B R_B = 5 - (0.00043)(10,000) = 5 - 4.3 = 0.7\ \text{V}$$ 7. **Step 5: Calculate $V_{CB}$** $$V_{CB} = V_C - V_B = 3.55 - 0.7 = 2.85\ \text{V}$$ **Final answer:** $$\boxed{V_{CB} = 2.85\ \text{V}}$$