A capacitor with plates separated by distance d is charged to a voltage difference AVc. All wires and batteries are disconnected, then the two plates are pulled apart $($with insulated handles so charges cannot flow$)$ to a new separation distance $2$d$.$ For each of the following quantities, how does it change $($i$.$e$.,$ double, half, unchanged, etc.$)$ when the separation distance doubles? Either write an equation that supports your conclusion or briefly explain your result. a$.$ Capacitance of the capacitor, C$.$