How are Kirchoff\'s laws written for the loops and what are the frequencies or n

Question

How are Kirchoff's laws written for the loops and what are the frequencies or normal modes of the system?

Explanation / Answer

Let's take the above example There are two kirchoff's laws 1)voltage law 2)current law You can use any one method to find out circuit parameters 1) for the voltage law you have to identify different loops (note identification of loops is not as straightforward as it seems there is a whole chapter dedicated to this in network theory) To solve a circuit it is enough if u can determine either all the currents through or voltages across individual branches. In the above case u can easily see that there are two individual loops (there is a third one which is a summation of other two) assume they have loop currents i1,i2 and they flow in anti clock direction in both loops (the loops i considered are L1->C1->C2->L2 and L2->C2->C3->L3) kirchoff voltage law states that in a loop the potential difference is zero (kind obvious) so write the votage eqns across each element with the currents assumed above L1di1/dt + C1*Integral of(i1dt) +C2*Integral of [(i1-i2)dt]+L2d(i1-i2)/dt =0 note current through second branch is i1 from top to bottom (anticlock) and i2 from bottom to top (again anti clock ) so resultant current is i1-i2 similarly u can write the other loop eqn two equations two unknowns the rest is mathematics 2)current law is bit a more simpler and easier. in this u assume voltages across individual elements and solve for the voltages In the case of above fig the V(L1)+V(C1)=V(L2)+V(C2)=V(L3)+V(C3) since they are in parallel( u have two equations here) now current law states that sum of currents entering or leaving a node is zero current in 1st branch is Integral(V(L1)dt/L1) = C1.d(V(C1))/dt =i1 (for sake of brevity ) similarly the currents in branches 2 and 3 can also written as i2,i3; here u have again 3 eqns in total now from current law i1+i2+i3=0;

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