A linear one-port has terminals t and the reference node (ground)

A linear one-port has terminals \(t\) and the reference node (ground). Inside the one-port, an independent voltage source of \(20.0\,\mathrm{V}\) has its positive terminal at node \(a\) and its negative terminal at ground; a \(5.00\,\Omega\) resistor connects \(a\) to node \(b\); a \(10.0\,\Omega\) resistor connects \(b\) to ground; and a \(4.00\,\Omega\) resistor connects \(b\) to \(t\). A voltage-controlled current source of transconductance \(0.200\,\mathrm{S}\) is directed from ground to \(t\); its controlling voltage is \(v_b\) (\(b\) with respect to ground), so the controlled current is \(0.200 v_b\). The controlled source remains active throughout. With the port open, determine \(V_\mathrm{th}=v_t\). With \(t\) connected to ground by an external short, define \(I_\mathrm{sc}\) as the current directed from \(t\) through that short to ground and determine \(I_\mathrm{sc}\). Then determine \(R_\mathrm{th}=V_\mathrm{th}/I_\mathrm{sc}\).

The dependent source stays on; \(R_\mathrm{th}\) is defined by the ratio of the two port measurements, not by resistor reduction with the independent source killed.