Question

Which of the following parameters in the series LCR circuit is analogous to driving force F in mechanics?
A. $\dfrac{{Vo}}{L}$
B. Inductance L
C. Capacitance C
D. Voltage $Vo$

Answer 1

As we know that there is an equation for forced oscillation in mechanics is:
$m\dfrac{{{d^2}x}}{{d{t^2}}} + b\dfrac{{dx}}{{dt}} + kx = F$
Similarly the LCR circuit equation is also similar to this equation, the equation is :
$L\dfrac{{{d^2}q}}{{d{t^2}}} + R\dfrac{{dq}}{{dt}} + \dfrac{q}{C} = Vo$

Complete step by step solution: We have studied in mechanics that force is responsible for acceleration of a body. Also we know that charge accelerates under the influence of an external electric field which in turn depends upon the potential difference across the space.
We can visualize this potential difference in comparison to Force if we take the example of water reservoirs on the top of every house. They are the source of potential difference for water due to which water flows in the pipes. The motion of water in pipes is similar to the motion of charge in the wires. Gravitational force is responsible for the flow of water and electric potential difference is responsible for the flow of charges.
So we can say that, the parameter which is analogous to driving force in mechanics is voltage because the difference in the voltage i.e. potential difference is the reason for working of a circuit (battery) like a force is needed to push or pull an object in mechanics.

Thus $Vo$ is analogous to driving force F in mechanics.

Note: $m\dfrac{{{d^2}x}}{{d{t^2}}} + b\dfrac{{dx}}{{dt}} + kx = F$ and $L\dfrac{{{d^2}q}}{{d{t^2}}} + R\dfrac{{dq}}{{dt}} + \dfrac{q}{C} = Vo$ these equations are the crux of this question .
One can easily correlate between these two equations and thus can deduce that $Vo$ is the analogous one.