Problem P. 4376. (October 2011)
P. 4376. Two capacitors of capacitances C_{1}=180 pF and C_{2}=20 pF were connected in series, and their free terminals were connected to the terminals of a rechargeable battery which could supply a constant e.m.f. of U_{0}=24 V. (The dielectric between the plates of both condensers was air.) Thus in both capacitors some energy was stored. Later the energy stored in the condensers was increased, with the same amount in both. This was done by filling totally the space between the plates of the capacitor of capacitance C_{2} by glass, the relative dielectric constant of which is _{r}. The connection of the capacitors and the other capacitor of capacitance C_{1} were not changed.
a) What was the relative dielectric constant _{r} of the glass which was used?
b) By what amount did the energy of the condensers increase? (The relative dielectric constant of air is 1.)
(5 pont)
Deadline expired on November 10, 2011.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. \(\displaystyle a)\) \(\displaystyle \varepsilon_{\rm r}=6.\)
\(\displaystyle b)\) Az egyes kondenzátorok energiaváltozása \(\displaystyle 7{,}8\cdot10^{9}\,{\rm J}\approx 8~{\rm nJ}.\)
Statistics:
55 students sent a solution.  
5 points:  Adrián Patrik, Agócs Fruzsina, Antalicz Balázs, Balogh Tamás, Bingler Arnold, Bojtár Orsika, Bolgár Dániel, Csáky Pál, Csóka József, Czipó Bence, Dinev Georgi, Filep Gábor, Fülep Andrea , Garami Anna, Gróf Gábor, Horicsányi Attila, Janzer Barnabás, Janzer Olivér, Jenei Márk, Juhász Péter, Kollarics Sándor, Koncz Gabriella, Laczkó Zoltán Balázs, Mázik László, Nagy Zsuzsika, Nánási József, Pataki Bálint Ármin, Sárvári Péter, Simig Dániel, Szabó 928 Attila, Székely Eszter, Szigeti Bertalan György, Szilágyi 585 Dezső, Tilk Bence, Ürge László, Vajda Balázs, Varga 555 Dávid, Virágh Anna. 
4 points:  Cseke Zsombor, Kovács 444 Áron, Öreg Zsombor, Seres Imre, Szélig Áron, Tuza Réka. 
3 points:  9 students. 
2 points:  2 students. 
