Question

The resonant frequency of a series LCR circuit is 'f'. The circuit is now connected to the sinusoidally alternating e.m.f of frequency '2f'. The new reactance X'_L and X'_C are related as ____________.

Options

• `"X'"_"C" = 1/4 "X'"_"L"`

• `"X'"_"C" = 2 "X'"_"L"`

• `"X'"_"C" = 1/2 "X'"_"L"`

• `"X'"_"C" =  "X'"_"L"`

Answer 1

The resonant frequency of a series LCR circuit is 'f'. The circuit is now connected to the sinusoidally alternating e.m.f of frequency '2f'. The new reactance X'_L and X'_C are related as `"X'"_"C" = 1/4 "X'"_"L"`.

Explanation:

`"At resonant frequency"  "X"_"L" = 2pi "fL", "X"_"C" = 1/(2pi"fL")  "and"  "X"_"L" = "X"_"C"`

`"when frequency is 2f,"  "X'"_"L" = 4 pi"fL", "X'"_"C"= 1/(4 pi"fC")`

`therefore "X"_"L" = 2 "X"_"L" and "X'"_"C" = "X"_"C"/2`

`"X'"_"C"/"X'"_"L" = 1/4`