Method 1
Here we plot the intersection of three functions g[8,pc], g[10,pc], g[20,pc] respect tof[pc].
For example,if we want to find the intersetion of g[8,pc] and y=f[x] when we plot g[8,pc], we can set the MeshFunction of g[8,pc] to y-f[x],that is MeshFunctions -> {#2 - f[#1] &}, Mesh -> {{0}}
np = 2; f[pc_] := 1; q[d_, pc_] := (pc/(100*0.48))* Sum[((Pi/4)*(d - (2*n*0.48))^2), {n, 1, np}]; p[d_] := Sum[Pi*(d - (2*n - 1)*0.48), {n, 1, np}]; g[d_, pc_] := q[d, pc]/p[d]; plot = Plot[Evaluate[Table[g[d, pc], {d, {8, 10, 20}}]], {pc, 0, 50}, MeshFunctions -> {#2 - f[#1] &}, Mesh -> {{0}}, MeshStyle -> {PointSize[Large], Automatic}, PlotRange -> All, AxesLabel -> {"%", "li/lp"}, FrameLabel -> {Style["pc", 12, Bold], Style["li/lp", 12, Bold]}, PlotLabels -> {"d=8", "d=10", "d=20"}, PlotTheme -> "Scientific", GridLines -> Automatic, PlotLabel -> "Razão comprimentos"] Show[plot, Plot[f[pc], {pc, 0, 50}]]
Method 2
On the other hand, we can also set three pure functions Table[Function[pc, g[d, pc] - f[pc] // Evaluate], {d, {8, 10, 20}}]
when we plot f[pc] to get the three intersections.
np = 2; f[pc_] := 1; q[d_, pc_] := (pc/(100*0.48))* Sum[((Pi/4)*(d - (2*n*0.48))^2), {n, 1, np}]; p[d_] := Sum[Pi*(d - (2*n - 1)*0.48), {n, 1, np}]; g[d_, pc_] := q[d, pc]/p[d]; Plot[f[pc], {pc, 0, 50}, MeshFunctions -> Table[Function[pc, g[d, pc] - f[pc] // Evaluate], {d, {8, 10, 20}}], Mesh -> {{0}}, MeshStyle -> Directive[PointSize[Large], Red]]
