can u plzzzzzzz tell easy way to solve the numerial  problems with the help of KIRCHOFF'S      RULES???????

AND WHAT ARE THE RULES  USED IN NUMERICAL PROBLEMSSS???? PLZZZZZZZZZZZZZZZ!!!!!!

Hi,
There are two Kirchoff’s laws. These are:
1.  Kirchoff’s first law or junction rule. It states that the algebraic sum of the currents meeting at a point in an electrical circuit is always zero.
2.  Kirchoff’s second rule or loop rule. It states that in any closed part of an electrical circuit, the algebraic sum of the e.m.fs is equal to the algebraic sum of the resistances and currents flowing through them.
Let’s learn to apply these rules using an example,
Consider your NCERT exercise problem 3.9.

 
Determine current in each branch of the circuit.
Solution:
Step1: spot junctions and then distribute current through them.
Ø Let current I flow in the circuit.
Ø We first encounter a junction at A.
Ø Distribute currents I1 towards point B and I-I1 towards point D.
Ø Then at junction B, current I1 enters into the junction and two currents I2 towards point C and I1-I2 towards D leaves it.
Ø At junction D, currents I-I1 and I1-I2 enters into it and a current (I-I1+I1-I2) = I-I2 leaves towards point C.
Ø At junction C, as two currents I2 and I-I2 enters into it through two branches and the third branch is the main branch of circuit in which current I flows.

Step2: Now select loops. As we have three unknowns I, I1 and I2 we need three loops.
Consider loop ABDA,

Using all the currents in the direction of the loop consider positive and those in the opposite direction are consider as negative (like, -5(I-I1) in branch DA). As there is no e.m.f. in the considered loop so the algebraic sum of the product of the resistances and current flowing through them is equal to zero.
Consider loop CBDC,
Consider loop ABCA,

Now solving above three equations, we get,

 
Now, current through,
Branch AB=I1=4/17A
Branch BC=I2=6/17A
Branch DC= (I-I2) =4/17A
Branch AD= (I-I1) =6/17A
Branch BD= (I1-I2) = - (2/17)A i.e. current flows in the opposite direction from D to B.
Total current I=10/17A

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