The differential equation for the current i(t) in the circuit of the figure is

A. $$2\frac{{{d^2}i}}{{d{t^2}}} + 2\frac{{di}}{{dt}} + i\left( t \right) = \sin t$$

B. $$\frac{{{d^2}i}}{{d{t^2}}} + 2\frac{{di}}{{dt}}2i\left( t \right) = \cos t$$

C. $$2\frac{{{d^2}i}}{{d{t^2}}} + 2\frac{{di}}{{dt}} + i\left( t \right) = \cos t$$

D. $$\frac{{{d^2}i}}{{d{t^2}}} + 2\frac{{di}}{{dt}} + i\left( t \right) = \sin t$$

Answer: Option C