In an RLC circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to :

Options

A. 4L
B. L/2
C. L/4
D. 2L

Answer

B

Explanation

The phenomenon of resonance is common among systems that have a tendency to oscillate at a particular frequency. This frequency is called the natural frequency an energy source, whose frequency is equal to the natural becomes large and resonance is said to occur.
At resonance, `X_(L)=X_(C)`
i.e. `omega_(r)L=(1)/(omega_(r)C)`
or `omega_(r)=(1)/(sqrt(LC))` or `2piv_(r)=(1)/(sqrt(LC))`
or `v_(r)=(1)/(2pisqrt(LC))`
or LC=constant (as V remain same)
`(L_(2))/(L_(1))=(C_(1))/(C_(2))` or `(L_(2))/(L)=(C)/(2C)` or `L_(2)=(L)/(2)`