CIKCCIT llll-Oh'V .l\l> ()/7:A'.;77('.V.//. c.ii.iii.rs <H7 



2. The sum of the currents enleriiii; aii\ br-iucli point in ilie net- 

 work is always zero. 



Let us now apply tliese hiws to an elementary rircuil in order lo 

 (ieiluee the physical sij^niUcance of the circuit elements. 



Consider an elementary circuit consisting of a resistance clement 

 K. an inductance element L and a cafiacity element C in series, and 

 let an electromotive force E be applieil to this circuit. If / denote the 

 current in the circuit, the resistance drop is Rf, the inductance drop 

 is Ldl (It and the drop across the condenser is Q/C where (J is the 

 charge on the conilenser. It is evident that Q and / are related by the 

 equation I=dQ dt or Q= \ Idt. Now apply KirchhofT's law relating 

 lo the drop around the circuit : it gives the equation 



RI + LdI dt + Q C = E. 



MiiliipK i)otli sides 1)\- /: we get 



The right hand side is clearly the rate at which the impressed force is 

 delivering energ>' to the circuit, while the left hand side is the rate 

 at which energj- is being absorbed by the circuit. The first term 

 RP is the rate at which electrical energy is being con\erted into heat. 

 Hence the resistance element may be defined as a device for con- 

 verting electrical energy into heat. The second term - - — LP is the 



rate of increase of the magnetic energ\-. Hence the inductance 

 element is a device for storing energ\- in the magnetic field. The 



third term -7- Q-'2C is the rate of increase of the electric energy. 



Hence the condenser is a device for storing energy in the electric field. 



In the foregoing we have isolated and idealized the circuit elements. 

 Actually, of course, ever\- circuit element dissipates some energy in 

 the form of heat and stores some energy in the magnetic field and 

 some in the electric field. The analysis of the actual circuit element, 

 however, into three ideal components is quite convenient and useful, 

 and should lead to no misconception if properly interpreted. 



Now consider the general form of network possessing n independent 

 meshes or circuits. Let us number these from 1 to «, and let the 

 corresponding mesh currents be denoted by /i. /j . . . . /„. Let 

 electromotive forces £1, Ez .... En be apj>lied to the n meshes or 

 circuits respectively. Let Ljj, R,j, Qj denote the total inductance, 



