discharge of capacitor through a current source

Question

Assume we have a cap connected to a current source that draws a current \$I_0\$. What time would it take to discharge the cap by a voltage \$V_t\$?

$$t=\frac{C \times V_t}{I_0}$$

Is this correct or am I wrong?

Answer 1

This is correct. The charge of the capacitor is given by: $$Q=CV$$ and for constant current \$I\$, the charge is $$Q=I\cdot t$$ So $$CV=I\cdot t$$ which leads to $$t=\frac{CV}{I}$$