1. **Problem Statement:** Given a circuit with two transistors Q1 and Q2, with current gains $\beta_1=100$ and $\beta_2=50$, and a 20 V power supply, find the voltages $V_{O1}$, $V_{O2}$ and currents $I_1$, $I_2$, $I_{C1}$, $I_{C2}$. 2. **Known values and components:** - $\beta_1=100$, $\beta_2=50$ - Power supply $V_{CC}=20$ V - Resistors: $R_1=50\text{ k}\Omega$, $R_2=80\text{ k}\Omega$, $R_3=0.5\text{ k}\Omega$, $R_4=0.1\text{ k}\Omega$, $R_5=10\text{ k}\Omega$ 3. **Assumptions and transistor relations:** - $I_C = \beta I_B$ - $I_E = I_C + I_B = (\beta + 1) I_B$ - Voltages at collector and emitter nodes can be found using Ohm's law and Kirchhoff's laws. 4. **Step 1: Calculate base currents $I_{B1}$ and $I_{B2}$** - Let $I_{B1} = I_B$ for Q1, $I_{B2} = I_b$ for Q2. 5. **Step 2: Express collector currents:** - $I_{C1} = \beta_1 I_{B1} = 100 I_{B1}$ - $I_{C2} = \beta_2 I_{B2} = 50 I_{B2}$ 6. **Step 3: Write KCL and KVL equations:** - At Q1 emitter (which is base of Q2): $$I_{E1} = I_{B2} = (\beta_1 + 1) I_{B1} = 101 I_{B1}$$ - At Q2 emitter resistor $R_4=0.1\text{ k}\Omega$: $$V_{E2} = I_{E2} R_4 = (\beta_2 + 1) I_{B2} \times 0.1 \times 10^3 = 51 I_{B2} \times 100 = 5100 I_{B2} \text{ volts}$$ 7. **Step 4: Calculate $I_1$ and $I_2$ using resistor currents:** - $I_1$ flows through $R_1=50\text{ k}\Omega$ and $I_2$ through $R_5=10\text{ k}\Omega$. 8. **Step 5: Calculate voltages $V_{O1}$ and $V_{O2}$:** - $V_{O1}$ is at collector of Q1 after $R_3=0.5\text{ k}\Omega$ resistor: $$V_{O1} = V_{CC} - I_{C1} R_3 = 20 - 100 I_{B1} \times 500 = 20 - 50000 I_{B1}$$ - $V_{O2}$ is at collector of Q2: $$V_{O2} = V_{CC} - I_{C2} R_3 = 20 - 50 I_{B2} \times 500 = 20 - 25000 I_{B2}$$ 9. **Step 6: Solve for $I_{B1}$ and $I_{B2}$ using circuit constraints:** - Using KCL and KVL, and given the current sources $I_1$ and $I_2$, solve the system: $$I_1 = I_{B1} + I_{C1} = I_{B1} + 100 I_{B1} = 101 I_{B1}$$ $$I_2 = I_{B2} + I_{C2} = I_{B2} + 50 I_{B2} = 51 I_{B2}$$ 10. **Final expressions:** - $I_1 = 101 I_{B1}$ - $I_2 = 51 I_{B2}$ - $V_{O1} = 20 - 50000 I_{B1}$ - $V_{O2} = 20 - 25000 I_{B2}$ - $I_{C1} = 100 I_{B1}$ - $I_{C2} = 50 I_{B2}$ These formulas allow calculation of all requested values once $I_1$ and $I_2$ are known or measured. **Note:** Without numerical values for $I_1$ and $I_2$, the problem is expressed in terms of $I_{B1}$ and $I_{B2}$ as above.