Question

Two identical air-filled parallel-plate capacitors C₁ What is the charge on capacitor C₁ after the dielectric is inserted? and C₂ are connected in series to a battery that has voltage V. The charge on each capacitor is Q₂ . While the two capacitors remain connected to the battery, a dielectric with dielectric constant K>1 is inserted between the plates of capacitor C₁ , completely filling the space between them.

Answer 1

In Physics, when a dielectric material with a dielectric constant K is inserted into one of the capacitors connected to a battery, the capacitance increases by K, and since the voltage remains constant, the charge on the capacitor increases to K times the original charge.

Step-by-step explanation:

The question pertains to the field of Physics, particularly focusing on the behavior of capacitors when a dielectric material is inserted into one of them while connected to a battery. Initially, both capacitors C₁ and C₂ have an equal charge Q from the battery. Once the dielectric material with the dielectric constant K is inserted into C₁ and the capacitors remain connected to the battery, the capacitance of C₁ increases by a factor of K. This is because the capacitance of an empty capacitor is increased by a factor equal to the dielectric constant (K) when the space between its plates is filled by the dielectric material. Given that the voltage across the capacitors remains constant (since they are still connected to the battery), the charge on C₁ must increase to Q₁ = K×Q.