Respuesta :
Answer:
k = 2.45
Explanation:
It is given that,
Charge acquired on each plate of the capacitor due to a battery, [tex]q=160\ \mu C[/tex]
If V is the potential difference across the plates, capacitance in air is given by :
[tex]C_a=\dfrac{q}{V}=\dfrac{160}{V}[/tex].............(1)
Let k is the dielectric constant of the dielectric slab. While the battery connection is maintained, a dielectric slab is inserted into and fills the region between the plates. This results in the accumulation of an additional charge of 220 µC on each plate.
New charge becomes, [tex]Q=220\ \mu C+220\ \mu C=440\ \mu C[/tex]
[tex]C_d=\dfrac{Q}{V}=\dfrac{440}{V}[/tex].............(2)
The dielectric constant of the dielectric slab is given by :
[tex]k=\dfrac{C_d}{C_a}[/tex]
[tex]k=\dfrac{440}{160}[/tex]
k = 2.45
So, the dielectric constant of the dielectric slab is 2.45. Hence, this is the required solution.
