1. **Working principle of BJT:** A Bipolar Junction Transistor (BJT) works by using two junctions: emitter-base and base-collector. When the base-emitter junction is forward biased and base-collector is reverse biased, electrons/hole injection occurs causing current flow controlled by the base current. The small input current at the base controls a larger current flowing from emitter to collector. 2. **Common emitter amplifier circuit and proving $I_E = I_B + I_C$:** - The circuit has a transistor with emitter, base, and collector terminals. - The base current $I_B$ flows into the base. - The collector current $I_C$ flows from collector to emitter. - The emitter current $I_E$ is the sum of currents leaving/entering the emitter terminal. - By Kirchhoff's current law at the transistor junction, $$I_E = I_B + I_C$$ since the emitter current consists of both base and collector currents combined. 3. **Amplification process of BJT:** - The small base current $I_B$ controls the larger collector current $I_C$. - The BJT amplifies the input current signal as output current $I_C = \beta I_B$ where $\beta$ is current gain. - This results in a voltage and power gain in the circuit. 4. **Base current equation for voltage divider bias:** - Voltage divider bias circuit uses two resistors $R_1$ and $R_2$ connected to base. - Base voltage $$V_B = V_{CC} \times \frac{R_2}{R_1 + R_2}$$ - Applying Kirchhoff’s voltage law and considering base-emitter voltage $V_{BE}$ and emitter current relation, base current equation is $$I_B = \frac{V_B - V_{BE}}{R_B + (\beta + 1) R_E}$$ where $R_B$ is base resistor, $R_E$ is emitter resistor, and $\beta$ is transistor gain. 5. **Proof of $I_B = R_B + (\beta + 1)R_E$ and $V_{CE} = V_{CC} - I_C (R_C + R_E)$ in emitter bias circuit:** - Emitter bias circuit has resistors $R_B$, $R_C$, and $R_E$ connected appropriately. - Applying Kirchhoff's laws: $$I_B = \frac{V_{CC} - V_{BE}}{R_B + (\beta + 1) R_E}$$ - Collector-emitter voltage: $$V_{CE} = V_{CC} - I_C (R_C + R_E)$$ These equations follow from loop voltage equations and current relations in the transistor circuit.