Determine the values of r_p , μ , and g_m for a triode operating at...

From the given plate characteristics, we identify the operating point at $V_p = 200 \text{ V}$ and $V_g = -6 \text{ V}$. At this point, the plate current is $I_p = 3 \text{ mA}$.

To find the plate resistance $r_p$, we use the formula $r_p = \left( \dfrac{\Delta V_p}{\Delta I_p} \right)_{V_g = \text{constant}}$.
Keeping $V_g = -6 \text{ V}$ constant, we select two points on this curve from the dashed box: $(V_p = 200 \text{ V}, I_p = 3 \text{ mA})$ and $(V_p = 240 \text{ V}, I_p = 8 \text{ mA})$.
$r_p = \dfrac{240 - 200}{(8 - 3) \times 10^{-3}} = \dfrac{40}{5 \times 10^{-3}} = 8000 \Omega = 8.0 \text{ k}\Omega$.

To find the mutual conductance $g_m$, we use the formula $g_m = \left( \dfrac{\Delta I_p}{\Delta V_g} \right)_{V_p = \text{constant}}$.
Keeping $V_p = 200 \text{ V}$ constant, we select two points on this vertical line: $(V_g = -6 \text{ V}, I_p = 3 \text{ mA})$ and $(V_g = -4 \text{ V}, I_p = 8 \text{ mA})$.
$g_m = \dfrac{(8 - 3) \times 10^{-3}}{-4 - (-6)} = \dfrac{5 \times 10^{-3}}{2} = 2.5 \times 10^{-3} \text{ A/V} = 2.5 \text{ millimho}$.

To find the amplification factor $\mu$, we use the relation $\mu = r_p \times g_m$.
$\mu = (8.0 \times 10^3) \times (2.5 \times 10^{-3}) = 20$.

Alternatively, $\mu$ can be calculated directly from the graph using $\mu = -\left( \dfrac{\Delta V_p}{\Delta V_g} \right)_{I_p = \text{constant}}$.
Keeping $I_p = 3 \text{ mA}$ constant, we use points $(V_p = 200 \text{ V}, V_g = -6 \text{ V})$ and $(V_p = 160 \text{ V}, V_g = -4 \text{ V})$.
$\mu = -\dfrac{160 - 200}{-4 - (-6)} = -\dfrac{-40}{2} = 20$.

Thus, $r_p = 8.0 \text{ k}\Omega$, $\mu = 20$, and $g_m = 2.5 \text{ millimho}$.

Answer: $8.0 \text{ k}\Omega$, $20$, and $2.5 \text{ millimho}$