Physics
Physics
Problem
Two identical isolated parallel-plate capacitors initially hold the same charge at potential difference while filled with dielectric slabs. Capacitor X contains a slab with dielectric constant , and capacitor Y contains a slab with dielectric constant . In separate experiments, each dielectric is slowly and completely removed. What is the ratio of the external work required to remove the dielectric from capacitor Y to that required for capacitor X? a) b) c) d)Intuitive explanation
The key is recognizing that work done on a capacitor depends on how its energy changes as the dielectric leaves. Since both capacitors start isolated with the same charge , that charge stays constant during removal. As the dielectric constant decreases, the capacitance drops, forcing the voltage to rise—and the stored energy increases. The external work needed equals this energy increase. Because capacitor Y starts with a higher dielectric constant, it undergoes a larger relative change in capacitance and voltage, requiring more work to fully extract its dielectric.
Intuitive explanation
The key is recognizing that work done on a capacitor depends on how its energy changes as the dielectric leaves. Since both capacitors start isolated with the same charge , that charge stays constant during removal. As the dielectric constant decreases, the capacitance drops, forcing the voltage to rise—and the stored energy increases. The external work needed equals this energy increase. Because capacitor Y starts with a higher dielectric constant, it undergoes a larger relative change in capacitance and voltage, requiring more work to fully extract its dielectric.