5. A capacitor with capacitance $C$, charged to a voltage $U_{0}$, is connected through a resistor with resistance $R$ to an uncharged capacitor with capacitance $4 C$.
1) Find the current in the circuit immediately after connection.
2) Find the steady-state (after a long time) voltage on the capacitor with capacitance $C$.
3) How much heat will be dissipated in the circuit after connection.
5. 
1) $I_{0}=\frac{U_{0}}{R}$
2) Law of charge conservation:

$$
C U_{0}=C U+4 C U \Rightarrow U=\frac{U_{0}}{5}
$$

![](https://cdn.mathpix.com/cropped/2024_05_06_4d7aec0c8bbef904a8ecg-4.jpg?height=206&width=663&top_left_y=248&top_left_x=1256)
3) $Q=\frac{C U_{0}^{2}}{2}-\frac{(C+4 C) U^{2}}{2}=\frac{C U_{0}^{2}}{2}-\frac{5 C U_{0}^{2}}{2 \cdot 25}=\frac{2}{5} C U_{0}^{2}$