A concealed circuit (black box) consisting of resistors has four terminals (Fig.). If a voltage is applied between clamps 1 and 2 when clamps 3 and 4 are disconnected, the power liberated is N 1 = 40 W, and when the clamps 3 and 4 are connected, the power liberated is N 2 = 80 W. If the same source is connected to the clamps 3 and 4, the power liberated in the circuit when the clamps 1 and 2 are disconnected is N 3 = 20 w.
Determine the power N 4 consumed in the circuit when the clamps 1 and 2 are connected and the same voltage is applied between the clamps 3 and 4.
Text Solution
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Sol. Let us make use of the fact that any "black box" circuit consisting of resistors can be reduced to a form (Fig.), where the quantities R 1 , R 2 , ….. R 5 are expressed in terms of the resistances of the initial resistors of the "black box" circuit (this can be verified by using in the initial circuit the transformations of the star-delta type and reverse transformations). By hypothesis, equal currents pass each time through resistors of resistance R 1 and R 4 and also through R 3 and R 5 (or there is no current through them when the clamps are disconnected).
Using circumstance, we can simplify the circuit as shown in Fig. Then, by hypothesis,
N 1 = 
, N 2 = 
,
N 3 = 
, N 4 = 
,
It can easily be verified that
N 1 N 4 = N 2 N 3 .
Consequently,
N 4 = 
= 40 W.
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