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
Calling [tex]C_1[/tex] the capacitance of capacitor 1 and [tex]V_1[/tex] its potential difference, the energy stored in capacitor 1 is
[tex]U=\frac{1}{2}C_1 V_1^2[/tex]
For capacitor 2, we have:
- The capacitance is half that of capacitor 1: [tex]C_2 = \frac{C_1}{2}[/tex]
- The voltage is twice the voltage of capacitor 1: [tex]V_2 = 2 V_1[/tex]
so the energy stored in capacitor 2 is
[tex]U_2 = \frac{1}{2}C_2 V_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]
