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

The network shown is assembled with uncharged capacitors $X , Y$ , and $Z$ , with $C X = 4.0 \mu F , C Y =$ $6.0 \mu \mathrm { F }$ , and $\mathrm { C } _ { \mathrm { Z } } = 5.0 \mu \mathrm { F }$ . 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 $\mathrm { S } _ { 2 }$ is kept open. What is the final potential difference across capacitor $\mathrm { X }$ ?

A) $60 \mathrm {~V}$
B) $120 \mathrm {~V}$
C) $67 \mathrm {~V}$
D) $75 \mathrm {~V}$
E) $82 \mathrm {~V}$

Correct Answer:

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