The Network Shown Is Assembled with Uncharged Capacitors X $C _ { X } = 3.0 \mu \mathrm { F } \text {, }$

The network shown is assembled with uncharged capacitors X , Y, and Z, with $C _ { X } = 3.0 \mu \mathrm { F } \text {, }$ $\mathrm { C } _ { \mathrm { Y } } = 5.0 \mu \mathrm { F }$ and $C _ { Z } = 1.0 \mu \mathrm { F }$ The switches S₁ and S₂ are initially open, and a potential difference V_ab = 120 V is applied between points a and b. After the network is assembled, switch S₁ is then closed, but switch S₂ is kept open. What is the final potential difference across capacitor Z?

A) 100 V
B) 600 V
C) 55 V
D) 38 V
E) 29 V