A given `LCR` series circuit satisfes the condition for resonance with a given `AC` source. If the angular frequency of the `AC` source is increased by `100%` then in order to establish resonance, and without changing the value of inductance, capacitance must be

Options

A. Increased by `100%`
B. Reduced by `50%`
C. Increased by `75%`
D. Reduced by `75%`

Explanation

At resonance, `omegaL=(1)/(omegaC)`, in second case for resonance, `2omegaL=(1)/(2omegaC')`
`:. C'=(1)/(4omega^(2)L)=(LC)/(4L)=(C )/(4)`
`:. (DeltaC)/(C )=(3)/(4)`