what is the effective resistance across A and B?

Asked by lambahisar | 18th 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 | 19th Apr, 2020, 12:07: PM