Find the resistance between a&b
Asked by hrittik12d
13th September 2018,
11:49 AM
Answered by Expert
Answer:
Let us apply a potential difference V across the points A and C. Let i be the current drawn by the given resistance network.
At the point A, current branches as x and (i-x) as shown in figure. Due to symmetry at point C , we will have currents (i-x)
and x merge together so that net current i is leaving from the network. It should be noted here the current components
are reversed at outlet between top and bottom branch compare to inlet.
It can be worked out that current (2x-i) is passing through 3R resistance.
if we apply Kirchoff's Voltage Law(KVL) in the loop ABCA, we get, 2R×(i-x) + R x = V ................(1)
if we apply KVL for the loop ADBA, we get R x + 3R×(2x-i) = 2R×(i-x) .....................(2)
By solving (1) and (2), we get x = (5/9)×i .................(3)
By substituting for x in eqn.(1), we get the equivalent resistance, ( V / i ) = (13/9)×R
Answered by Expert
13th September 2018,
8:33 PM
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