I have a some what basic question. I was just brushing up on some basics with a book on fundamentals of electric circuits. I came across this:

[![enter image description here](https://i.stack.imgur.com/DY4Kg.png)](https://i.stack.imgur.com/DY4Kg.png)

They say that Fig 7.40a with a switch can be replaced by figure 7.40b where u(t) is the unit step function. I don't understand that. For t < 0, that voltage source will be producing 0V -> hence a short between the resistor and the negative plate of the capacitor. Wouldn't that cause the initial voltage on the capacitor to flow through the resistor?

**To me, it seems like it's only possible to jump from Fig 7.40a to 7.40b if the initial voltage on the capacitor is 0V. Am I missing something?**