To find the voltage across the capacitor, we can use the fundamental relationship between the energy stored in a capacitor, the charge on the plates, and the voltage across it. This relationship is given by the formula:
[tex]\[ V = \frac{E}{Q} \][/tex]
where:
- [tex]\( V \)[/tex] is the voltage across the capacitor,
- [tex]\( E \)[/tex] is the energy stored in the capacitor,
- [tex]\( Q \)[/tex] is the charge on the plates.
Given the values:
- [tex]\( E = 7.77 \times 10^{-7} \)[/tex] Joules,
- [tex]\( Q = 4.29 \times 10^{-8} \)[/tex] Coulombs,
we can substitute these values into the formula to find the voltage [tex]\( V \)[/tex].
[tex]\[ V = \frac{7.77 \times 10^{-7} \ \text{J}}{4.29 \times 10^{-8} \ \text{C}} \][/tex]
Dividing the energy by the charge:
[tex]\[ V \approx 18.111888111888113 \ \text{Volts} \][/tex]
Thus, the voltage across the capacitor is approximately [tex]\( 18.11 \)[/tex] Volts.
