A capacitor is connected to a fixed-voltage source V. If a dielectric with dielectric constant κ is inserted between plates, how do C, Q, and V change?

A capacitor is connected to a fixed-voltage source V. If a dielectric with dielectric constant κ is inserted between plates, how do C, Q, and V change?

• A. C' = κ C; Q' = κ C V; V remains V
• B. C' = κ C; Q' = C V; V remains V
• C. C' = κ C; Q' = κ C V; V increases
• D. C' = κ C; Q' = κ C V; V decreases

Answer: (A)

When a dielectric with dielectric constant κ is inserted between the plates of a capacitor connected to an ideal voltage source, the capacitance increases by κ: C' = κ C. The ideal voltage source fixes the voltage across the capacitor, so V remains the same: V' = V. Since charge is Q = C V, the new charge becomes Q' = C' V' = (κ C) V = κ C V. So the dielectric increases capacitance and the stored charge by κ, while the voltage stays fixed.

When a dielectric with dielectric constant κ is inserted between the plates of a capacitor connected to an ideal voltage source, the capacitance increases by κ: C' = κ C. The ideal voltage source fixes the voltage across the capacitor, so V remains the same: V' = V. Since charge is Q = C V, the new charge becomes Q' = C' V' = (κ C) V = κ C V.

So the dielectric increases capacitance and the stored charge by κ, while the voltage stays fixed.