Answer:
a
[tex]U = 3.505 *10^9 \ J[/tex]
b
[tex]U_1 = 7.696 *10^9 \ J[/tex]
Explanation:
From the question we are told that
The capacitance is [tex]C = 1.89 \ F[/tex]
The voltage is [tex]V = 60.9 \ k V = 60.9 *10^{3} \ V[/tex]
The first dielectric constant is [tex]\epsilon_1 = 431[/tex]
The second dielectric constant is [tex]\epsilon_2 = 947[/tex]
Generally the electric potential energy is mathematically represented as
[tex]U = \frac{1}{2} * C * V^2[/tex]
=> [tex]U = \frac{1}{2} * 1.89 * (60.9 *10^{3})^2[/tex]
=> [tex]U = 3.505 *10^9 \ J[/tex]
Generally the capacitance when the capacitor's filling was changed is
[tex]C_n = 1.89 * \frac{947}{431}[/tex]
=> [tex]C_n = 4.15[/tex]
Generally the electric potential energy when the capacitor's filling was changed is
[tex]U_1 = \frac{1}{2} * C_1 * V^2[/tex]
=> [tex]U_1 = \frac{1}{2} * 4.15 * (60.9 *10^{3})^2[/tex]
=> [tex]U_1 = 7.696 *10^9 \ J[/tex]
