BJT circuit analysis
For parts c) and d), try the following.

Step 1) Using nodal analysis, derive an equation whose terms include the unknown voltage at node \$V_Z\$ in Figure 1 below. [Hint: Apply KCL at the \$V_Z\$ node.] Note that "\$I_B\$" will be one of the terms in your nodal analysis equation. (You'll replace the \$I_B\$ term in the next step.)







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1.

Step 2) In your nodal analysis equation from step 1, replace \$I_B\$ with an equivalent term that includes \$V_O\$ (whose value is unknown) and other terms whose values are known:

$$
I_{RL}=I_E=I_C+I_B=\beta I_B+I_B=I_B(\beta +1)=V_O/R_L
\\[0.2in]
\rightarrow I_B=\frac{V_O}{R_L(\beta +1)}
$$

Step 3) You'll need a second equation to solve for the two unknowns \$V_Z\$ and \$V_O\$:

$$
V_O=V_Z+V_{EB}
$$

Step 4) You now have two equations and two unknowns \$V_Z\$ and \$V_{O}\$. Using the method of simultaneous equations solve for the two unknowns \$V_Z\$ and \$V_{O}\$.