Question

The natural frequency of an LC circuit is 125 kHz. When the capacitor is totally filled with a dielectric material, the natural frequency decreases by 25 kHz. Dielectric constant of the material is nearly.

Options

• 3.33

• 2.12

• 1.56

• 1.91

Answer 1

1.56

Explanation:

`"Frequency ofoscillation, f" = 1/(2pi sqrt"LC")`

`therefore "f" prop 1/sqrt"C"`

`therefore f_"air"/f_"dielectic" = sqrt ("C"_"dielectic"/"C"_"air")`

`"But"  "C"_"dielectic"/"C"_"air" = "K"`    ....(k = dielectric constant)

`therefore "f"_"air"/"f"_"dielectic" = sqrt"K"`

`125/100 = sqrt"K"`

`therefore "K" = (5/4)^2`

`therefore "K" = 1.56`