Mathematical and Physical Journal
for High Schools
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Problem P. 4968. (October 2017)

P. 4968. The heating elements of an electric heater can be connected as shown in the figure. When voltage is applied across points \(\displaystyle A\) and \(\displaystyle B\), then during a certain amount of time, water of mass \(\displaystyle m\) can be boiled. How much water can be boiled during the same amount of time when the voltage is applied across points \(\displaystyle B\) and \(\displaystyle C\) or across points \(\displaystyle C\) and \(\displaystyle A\)?

(4 pont)

Deadline expired on November 10, 2017.

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

Megoldás. Az egyes pontpárok közötti eredő ellenállás:

\(\displaystyle R_{AB}=\frac9{14}R,\qquad R_{BC}=\frac87\,R,\qquad R_{AC}=\frac32 R.\)

Adott feszültség mellett a leadott teljesítmény, és ezzel együtt a felforralható víz mennyisége az eredő ellenállásokkal fordítottan arányos:

\(\displaystyle m_{AB}=m,\qquad m_{BC}=\frac9{16}\,m\approx0{,}56\,m ,\qquad m_{AC}=\frac{3}{7}\,m\approx0{,}43\,m.\)


83 students sent a solution.
4 points:54 students.
3 points:20 students.
2 points:5 students.
1 point:2 students.
0 point:2 students.

Problems in Physics of KöMaL, October 2017