Question
For the network shown in fig. below. Calculate the equivalent resistance between points A and B.
Solution
The distribution of current in the circuit will be as shown in fig. below, following Kirchhoff’s first law.
Here point F is not a true junction, hence is shown separate.
If R’ is the effective resistance of circuit between A and B, then
E = IR’ ...(i)
In a closed circuit EABE
E = (I – I1) R + (I – I1) R
= 2 (I – I1) R ... (ii)
In a closed circuit GDCG,
I2 R/2 + R I2/2 – (I1 – I2) R = 0
I2 = I1/2 ...(iii)
In a closed circuit AGCBA, we have
[from (iii)]
Putting this value in (ii) we get
...(iv)
Comparing (i) and (iv) we get
