Question

Two capacitors are identical, except that one is empty and theother is filled with a dielectric (κ = 3.60). The empty capacitor is connected to a24.0 V battery. What must be thepotential difference across the plates of the capacitor filled witha dielectric such that it stores the same amount of electricalenergy as the empty capacitor?

Answer 1

Answer:

Explanation:

Given

Two capacitor are identical such that one is empty and other is filled with dielectric

Inserting a dielectric increases the capacitance k times if k is the dielectric strength

Empty capacitor $C_1=C$

Dielectric capacitor $C_2=k\times C=3.6C$

$V_1=24 V$

Energy stored in first capacitor $E_1=\frac{1}{2}CV^2=\frac{1}{2}\times C(24)^2$

Energy stored in second capacitor $E_2=\frac{1}{2}\times 3.6C\times (V)^2$

$E_1=E_2$

$\frac{1}{2}\times C(24)^2=\frac{1}{2}\times 3.6C\times (V)^2$

$V=12.64\ V$