Question

In LCR circuit the inductance is changed from L to 9L. For same resonant frequency the capacitance should be changed from C to ____________.

Options

• 9C

• `"C"/9`

• `"C"/3`

• 3C

Answer 1

In LCR circuit the inductance is changed from L to 9L. For same resonant frequency the capacitance should be changed from C to `"C"/9`.

Explanation:

`omega = 1/sqrt("L"_1 "C"_1) = 1/sqrt("L"_2 "C"_2)`

`therefore "L"_1 "C"_1 = "L"_2 "C"_2`

`"C"_2 = ("L"_1"C"_1)/"L"_2`

`= "L"/(9"L") xx "C"`

`= "C"/9`