The Network Shown Is Assembled with Uncharged Capacitors $X , Y$

The network shown is assembled with uncharged capacitors $X , Y$ , and $Z$ , with $C _ { X } = 3.0 \mu F$ , $C _ { Y } = 5.0 \mu \mathrm { F }$ and $\mathrm { C } _ { Z } = 1.0 \mu \mathrm { F }$ . The switches $\mathrm { S } _ { 1 }$ and $\mathrm { S } _ { 2 }$ are initially open, and a potential difference $V _ { a b } = 120 \mathrm {~V}$ is applied between points $a$ and $b$ . After the network is assembled, switch $\mathrm { S } _ { 1 }$ is then closed, but switch $S _ { 2 }$ is kept open. What is the final potential difference across capacitor $Z$ ?

A) $38 \mathrm {~V}$
B) $100 \mathrm {~V}$
C) $29 \mathrm {~V}$
D) $55 \mathrm {~V}$
E) $600 \mathrm {~V}$