How does the voltage division on this work?
So in this particular circuit, we can see that the overall voltage across the RC branch of the circuit containing V&phi; is equal to Vo. Given this fact, we can then use the impedances of the resistor and the capacitor to determine V&phi;. The voltage division rule for two series impedances Z1 and Z2 (where Z2 is tied to ground) is given by: $$ V_o = \frac{Z_2}{Z_1+Z_2}V_{source}  $$If this is true, we can identify both the bottommost wire in the diagram as ground and the capacitor as Z2 in our voltage divider equation (which, consequently, leaves the resistor as Z1). Given this information, the equation for V&phi; becomes: $$ V_{\phi} = \frac{\frac{10^4}{s}}{50+\frac{10^4}{s}}V_o $$ From here, we can multiply this equation by 1,which is the same as multiplying both top and bottom by s, which transforms the equation into: $$ V_\phi = \frac{10^4}{50s+10^4}V_o $$ Hope this was helpful!