6. (15 points) A capacitor with capacitance $C_{1}=20$ μF is charged to a voltage $U_{1}=20$ V. A second capacitor with capacitance $C_{2}=5$ μF is charged to a voltage $U_{2}=5$ V. The capacitors are connected with their oppositely charged plates. Determine the voltage that will establish across the plates.
Answer: 15 V.

Solution. Law of conservation of charge: $C_{1} U_{1}-C_{2} U_{2}=C_{1} U+C_{2} U$. We obtain:

$$
U=\frac{C_{1} U_{1}-C_{2} U_{2}}{C_{1}+C_{2}}=\frac{20 \cdot 20-5 \cdot 5}{20+5}=15 \mathrm{~V}
$$