To find the voltage across the capacitor, we can use the relationship between the energy stored, the charge, and the voltage across the capacitor. This relationship is given by the formula:
[tex]\[ V = \frac{W}{Q} \][/tex]
where:
- [tex]\( V \)[/tex] is the voltage across the capacitor,
- [tex]\( W \)[/tex] is the energy stored in the capacitor, and
- [tex]\( Q \)[/tex] is the charge on the plates of the capacitor.
In this problem, we are provided with:
- The energy [tex]\( W = 7.77 \times 10^{-7} \)[/tex] Joules,
- The charge [tex]\( Q = 4.29 \times 10^{-8} \)[/tex] Coulombs.
Using the formula, we plug in the given values:
[tex]\[ V = \frac{7.77 \times 10^{-7}}{4.29 \times 10^{-8}} \][/tex]
By performing the division, we find that the voltage across the capacitor is:
[tex]\[ V \approx 18.11188811188811 \][/tex]
Thus, the voltage across the capacitor is approximately [tex]\( 18.11188811188811 \)[/tex] volts.
