The Mathematical Theory of Electricity And Magnetism
The Mathematical Theory of Electricity And Magnetism
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Or, again, the solution of any dynamical problem is contained in the statement that the "action" is a minimum, while in thermodynamics the equilibrium state of any system can be expressed by the condition that the "entropy" shall be a maximum. It will now be shewn that the function which expresses the total rate of generation of heat plays a similar role in the theory of steady electric currents.
357. THEOREM. When a steady current flows through a network of conductors in which no discontinuiti...es of potential occur (and which, therefore, contains no batteries), the currents are distributed in such a way that the rate of generation of heat in the network is a minimum, subject only to the conditions imposed by Kirchhoff's first law; and conversely.
To prove this, let us select any closed circuit PQR ... P in the network, and let the currents and resistances in the sections PQ, QR, ... Be # 15 # 2 and R lt jR 2 > ____ Let the currents and resistances in those sections of the net- work which are not included in this closed circuit be denoted by x a, x b, ...
What to read after The Mathematical Theory of Electricity And Magnetism?
You can find similar books in the "Read Also" column, or choose other free books by James Hopwood Jeans to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Or, again, the solution of any dynamical problem is contained in the statement that the "action" is a minimum, while in thermodynamics the equilibrium state of any system can be expressed by the condition that the "entropy" shall be a maximum. It will now be shewn that the function which expresses the total rate of generation of heat plays a similar role in the theory of steady electric currents.
357. THEOREM. When a steady current flows through a network of conductors in which no discontinuiti...es of potential occur (and which, therefore, contains no batteries), the currents are distributed in such a way that the rate of generation of heat in the network is a minimum, subject only to the conditions imposed by Kirchhoff's first law; and conversely.
To prove this, let us select any closed circuit PQR ... P in the network, and let the currents and resistances in the sections PQ, QR, ... Be # 15 # 2 and R lt jR 2 > ____ Let the currents and resistances in those sections of the net- work which are not included in this closed circuit be denoted by x a, x b, ...
What to read after The Mathematical Theory of Electricity And Magnetism?
You can find similar books in the "Read Also" column, or choose other free books by James Hopwood Jeans to read onlineMoreLess
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