An ideal independent DC source V_S=12.0 V has its positive terminal at node s and its…

An ideal independent DC source \(V_S=12.0\,\mathrm{V}\) has its positive terminal at node \(s\) and its negative terminal at the reference node \(0\). Resistor \(R=2.20\,\mathrm{k}\Omega\) is connected from \(s\) to node \(a\). A silicon diode \(D\) has its anode at \(a\) and its cathode at \(0\). Define \(v_D=v_{a0}\) and define \(i_D\) as the current entering the anode. Use the piecewise-linear diode model: off is an open circuit requiring \(v_D\le 0.720\,\mathrm{V}\); on requires \[ v_D=0.720\,\mathrm{V}+i_D r_f,\qquad r_f=25.0\,\Omega,\qquad i_D\ge 0. \] Ignore leakage, breakdown, and capacitance. (a) Write the load-line equation relating \(i_D\) and \(v_D\). Determine the open-circuit intercept \((v_D,i_D)=(V_{\mathrm{oc}},0)\) and the short-circuit intercept \((v_D,i_D)=(0,I_{\mathrm{sc}})\). (b) Intersect the load line with the on-characteristic and compute the candidate operating point \((V_D,I_D)\). Verify the on-region inequalities. Report \(V_D\), \(I_D\), the voltage across \(R\) with plus at \(s\), and the power absorbed by \(D\) and by \(R\). (c) Repeat (a) and (b) after \(R\) is replaced by \(220\,\Omega\), with every other parameter unchanged. (d) A laboratory partner plots the first load line as the straight segment joining \((v,i)=(0,12.0\,\mathrm{V})\) to \((12.0\,\mathrm{V},0)\) on the \(i\)--\(v\) plane of the diode. Identify the coordinate error, state the correct intercepts, and determine whether that error would have changed the accepted region in (b).

The load line is KVL on the source–resistor–diode loop; the diode characteristic is a second line (or an open-circuit vertical) in the same plane.