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what is the effective resistance across A and B?
Asked by lambahisar | 18 Apr, 2020, 06:56: PM
Expert Answer
Let us connect a 9 V battery across A and B of given resistance network. Current distribution in the network is shown in figure.
If we apply Kirchoff's Voltage Law ( KVL ) to the loop A-B-Battery-A , we get, 18 i1 = 9 or i1 = 0.5 A ..................(1)
If we apply Kirchoff's Voltage Law ( KVL ) to the loop A-C-B-Battery-A , we get,
4 i2 + 3 ( i2 + i4) = 9 or 7 i2 + 3 i4 = 9 ............................ (2)
If we apply Kirchoff's Voltage Law ( KVL ) to the loop A-D-B-Battery-A , we get,
9 i3 + 10.8 ( i3 - i4) = 9 or 19.8 i3 - 10.8 i4 = 9 ............................ (3)
If we apply Kirchoff's Voltage Law ( KVL ) to the loop A-D-C-A , we get,
9 i3 + 6 i4 - 4 i2 = 0 ............................ (4)
By solving equations (2), (3) and (4), we get i2 = 1.266 A , i3 = 0.479 A and i4 = 0.0456 A
As seen from figure, total current drawan from 9V battery , i1 + i2 + i3 = ( 0.5 + 1.266 +0.479 ) A = 2.245 A
Hence equivalent resistance = 9 V / 2.245 A = 4 Ω
Answered by Thiyagarajan K | 19 Apr, 2020, 12:07: PM
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