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CBSE Class 12-science Answered

Find the equivalent resistance between the points a and b 
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Asked by prakriti12oct | 18 Jul, 2019, 09:10: AM
answered-by-expert Expert Answer
Let us apply a potential difference across a and b .  Let i be the net current flowing through the circuit.
At point-a, current divides into three parts, i.e., current i1 is passing through 10Ω resistor ,
current i2 is pasing through 5Ω resistor connected between point-a and point-e,
current i3 is pasing through 5Ω resistor connected between point-a and point-d.
 
if total current i is getting divded as i1 , i2 and i3 at point-a, then  currents should combine in same manner at point b.
 
hence at point-b, current i1 should come from 10Ω resistor, current i2 should come from 5Ω resistor connected across e and b ,
current i3 should come from 5Ω resistor connected across c and b.
Due to this symmetrical division and combining of currents at point-a and point-b, current flow from point-d to point-c is (i3 - i1)
 
After knowing the currents passing through all the resistors, we apply kirchoff's law to get currents i1 , i2 and i3 .
 
In the path of points a-e-b, we have,  10×i2 = V  ...........................(1)
In the path of points a-c-b, we have,   10×i1 + 5×i3 = V ......................(2)
In the closed loop of poits a-c-e-d-a, we have, -10×i1 + 5×(i3 - i1) + 5×i3 = 0   ..................(3)
 
By solving tha above three equations we get,  i1 = (2/35)V  ,  i2 = V/10 ,  i3 = (3/35)V  
 
Hence total current, i = i1 + i2 + i3 = [ (2/35)+(1/10)+(3/35)] V = (17/70)V  
 
or   effective resistance across a nd b = V/i  = (70/17)Ω ≈ 4.1 Ω
Answered by Thiyagarajan K | 18 Jul, 2019, 11:29: AM
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