The equivalent resistance between A and B of the network shown in figure is:
(a) 3R ohm
(b) (3/2)R ohm
(c) 2R ohm
(d) (2/3)R ohm
Answers
Answer:
In this case, the 2 resistors of 3 ohms and 2 ohms on the upper half of the circuit are connected in series and the combined resistance R1 is given as 3+2 = 5 ohms.
The 2 resistors of 6 ohms and 4 ohms on the lower half of the circuit are connected in series and the combined resistance R2 is given as 6+4 = 10 ohms.
The resistances R1, R2 and 30 ohms in the middle are connected in parallel. So the total resistance R of this parallel connection is given as
5
1
+
10
1
+
30
1
=
0.33
1
=3ohms. That is, the resistance in the closed loop is reduced to 3 ohms.
Hence, the value of the resistance in the circuit between A and B is 3 ohms.
Explanation:
8Ω and 2Ω are parallel.
R
1
1
=
8
1
+
2
1
=
8
5
∴R
1
=
5
8
From point B,
4Ω and 6Ω are parallel.
R
2
1
=
4
1
+
6
1
=
12
5
∴R
2
=
5
12
Now,
R
1
=
5
8
Ω,R
2
=
5
12
Ω are in series
∴R=
5
8
+
5
12
=4Ω
Now,
4Ω,3Ω,6Ω are parallel to each other.
∴
R
AB
1
=
4
1
+
3
1
+
6
1
=
12
9
=
4
3
∴R
AB
=
3
4
Ω
I know that this is not helpful to you but sorry