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P. 4273. Two unknown impedances are connected in parallel to the mains, of voltage 230 V and of frequency 50 Hz. The maximum value of the current in the main branch is 20 A. The current through one of the impedances leads the current in the main branch by an angle of , and through the other impedance the current lags behind the current in the main branch by an angle of .

a) What are the instantaneous current values in the two branches at t=0.01 s, if the current in the main branch is zero at t=0?

b) What are the values of the inductance and the capacitance in the two branches?

(5 points)

Deadline expired on 11 October 2010.

Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás. $\displaystyle a)$ A fõág pillanatnyi áramerõssége nulla, a mellékágaké $\displaystyle \pm 8{,}7~$A.

$\displaystyle b)$ Az egyik ágban lehet pl. egy 32,5 $\displaystyle \Omega$ értékû ohmos ellenállás, a másikban egy 60 mH induktivitású tekercs. Egy másik lehetõség: az egyik ágban egy $\displaystyle 100~\mu$F-os kondenzátor, a másikban 18,8 $\displaystyle \Omega$-os ellenállás.

Statistics on problem P. 4273.
 21 students sent a solution. 5 points: Bolgár Dániel, Börcsök Bence, Szabó 928 Attila, Várnai Péter, Virágh Eszter, Vuchetich Bálint. 4 points: Jéhn Zoltán, Laczkó Zoltán Balázs, Petõ János, Szemes Gábor Bence. 3 points: 4 students. 2 points: 7 students.

• Problems in Physics of KöMaL, September 2010

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