Q123 / 180 · KCET 2021 · Physics

$L C$-oscillations are similar and analogous to the mechanical oscillations of a block attached to a spring. The electrical equivalent of the force constant of the spring is

  • A
    reciprocal of capacitive reactance
  • B
    capacitive reactance
  • Correct answer
    C
    reciprocal of capacitance
  • D
    capacitance

Solution

For LC-oscillations, $L \frac{d i}{d t}+\frac{q}{C}=0$ Differentiating further it w.r.t $t$, we get $L \frac{d^{2} i}{d t^{2}}+\frac{I}{C}=0...(i)$ Similarly, for spring-block system, $m \frac{d^{2} x}{d t^{2}}+k x=0...(ii)$ Comparing Eqs. (i) and (ii), we get $m \propto L \text { and } k \propto \frac{1}{C}$

Hence, the correct answer is option: 'C'.

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