State the two rules that serve as general rules for analysis of electrical circuits. Use these rules to write the three equations that may be used to obtain the values of the three unknown currents in the branches (shown) of the circuit

Explanation

As per Kirchhoff.s first law the distribution of current in various branches of network are as shown in Fig.Applying Kirchhoff.s second law to mesh ABDA, we have
` - I_2. R_1 - (I_3 + I_2) R_3 - I_1 . r + E_1 = 0`
` rArr I_1 .r + I_2 (R_1 + R_3) + I_3 . R_3 = E_1` ....(i)
For mesh ACDA ,we have
` - (I_1 - I_2) R_2 + (I_3 + I_2 - I_1) R_4 - I_1.r + E_1 = 0`
` rArr I_1 (R_2 + R_4 + r) + I_2 (R_2 - R_4) - I_3.R_4 = E_1`
and for mesh `E_2 BDCE_2` , we have
`- I_3.r-(I_3 + I_2)R_3 - (I_3 + I_2 - I_1)R_4 + E_2 = 0`
` rArr - I_1.R_4 + I_2. (R_3 + R_4) + I_3.(r + R_3 + r_4) = E_2`
On simplifying these three equations we can find the value of currents flowing in various branches of the circuit