Please solve this question and show me how to do these
Asked by ankitabwn1999
20th September 2018,
1:05 PM
Answered by Expert
Answer:
Figure shows Step-by-Step evaluation of equivalent resistance of given resistance network.
In Step-1, we can see there is symmetry between resitances in top branch and resistances in bottom branch.
Due to symmetry the entering current i is getting divided into two equal parts i/2 and each equal part flows through
top branch and bottom branch.
Also in each branch there is a symmetry in entrance and exit. If the entering current i/2 in top branch is divided as i1 and i2 at entrance point B,
then in same way at exit point C, currents i1 and i2 merge to give combined current i/2.
This is due to symmetry. In same way at bottom branch also, if current i/2 is divided into i1 and i2 (again this is due to symmetry)
at entrance point A, then similar currents i1 and i2 combine at exit point D to give final current i/2.
This indicates, entire current flowing through the 10Ω resistor between B and O will flow towards the 10Ω resistor
connected between O and C without any division at O.
In same way, all the current flowing through 10Ω resistor between A and O will flow through 10Ω resistor connected
between O and D. Hence the top and bottom branches which are connected at O can be detached as shown in Step-2.
In step-2, we see that at each branch, 20Ω resistor is parallel with 5Ω resistor, and we can workout this equivalent resistance
of this parallel combination as 4Ω.
Hence at step-3, the given resistance network is reduced to parallel combination of two 4Ω resistors.
In step-4 this parallel combination two 4Ω resistor is worked out as 2Ω. Hence equivalent resistance of given network is 2Ω.
Then the current flowing in the circuit is 0.4/2 = 0.2A
Answered by Expert
20th September 2018,
9:04 PM
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