Mathematical and Physical Journal
for High Schools
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Problem P. 4273. (September 2010)

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 \frac{\pi}{3}, and through the other impedance the current lags behind the current in the main branch by an angle of \frac{\pi}{6}.

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 pont)

Deadline expired on October 11, 2010.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás. \(\displaystyle a)\) A főág pillanatnyi áramerőssége nulla, a mellékágaké \(\displaystyle \pm 8{,}7~\)A.

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


Statistics:

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, Pető János, Szemes Gábor Bence.
3 points:4 students.
2 points:7 students.

Problems in Physics of KöMaL, September 2010