Problem P. 4200. (November 2009)
P. 4200. Two alike discharge lamps are operated from the mains, 230 V and 50 Hz, and they are both connected to inductors in series. The inductors are alike. A condenser is connected in series to one of the discharge tubes. With this arrangement it is ensured that when the current through one of the lamps is maximum, then the current through the other one is minimum and viceversa. (Antistroboscopic navigation.) In both branch the RMS value of the power is 8 W. What is the total ohmic resistance of the discharge tube and the inductor together when the system is operated? Find the capacitance of the condenser and the inductance of the coils?
(5 pont)
Deadline expired on December 10, 2009.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. \(\displaystyle R=3{,}3\) k\(\displaystyle \Omega\); \(\displaystyle L=10{,}5~\)H; \(\displaystyle C=0{,}48~\mu\)F.
Statistics:
31 students sent a solution.  
5 points:  Béres Bertold, Bolgár Dániel, Galzó Ákos Ferenc, Hartstein Máté, Illés Dorottya, Janosov Milán, Jéhn Zoltán, Kaposvári István, Kungl Ákos Ferenc, Laczkó Zoltán Balázs, Lőrincz Dóra, Mayer Martin János, Pálovics Péter, Patartics Bálint, Pázmán Koppány, Roboz Klaudia, Szabó 928 Attila, Varju 105 Tamás, Vuchetich Bálint, Zsolczai Viktor. 
4 points:  Filep Gábor, Fonai Dániel. 
3 points:  1 student. 
2 points:  3 students. 
1 point:  1 student. 
0 point:  2 students. 
Unfair, not evaluated:  2 solutions. 
