Answer:
1/2
Explanation:
The energy stored in a capacitor is given by:
[tex]U=\frac{1}{2}CV^2[/tex]
where
C is the capacitance
V is the potential difference
For capacitor 1, we have
[tex]U_1=\frac{1}{2}C_1V_1^2[/tex]
Capacitor 2 has
[tex]C_2 = \frac{C_1}{2}[/tex] (half the capacitance of capacitor 1)
[tex]V_2 = 2 V_1[/tex] (twice the potential difference of capacitor 1)
So the energy of capacitor 2 is
[tex]U_2=\frac{1}{2}C_2V_2^2=\frac{1}{2}(\frac{C_1}{2})(2V_1)^2=C_1 V_1^2[/tex]
So, the ratio between the two energies is
[tex]\frac{U_1}{U_2}=\frac{\frac{1}{2}C_1 V_1^2}{C_1 V_1^2}=\frac{1}{2}[/tex]
