11 resistors are connected in network as shown in the figure. The equivalent resistance between A and B is: a) 2 ohm b) 3 ohm c) 1 ohm d) 5 ohm
Answers
Answer:
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 51+101+301=0.331=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.
To find:
Equivalent resistance between A and B.
Method:
This question can be easily solved using the potential method.
Step I: Connect an imaginary battery around points A and B
Step II: Write potential across each resistor. (Fig 1)
Step III: Rearrange the circuit.(Fig 2)
Step IV: Simplify and solve.
Please refer to the attachment first !!
⊕ Between A and X :
Five 25 ohm resistors are connected in parallel.
⇒ Rp = 25/5 = 5Ω
⊕ Between X and Y :
3 Ω and 6 Ω are connedted in parallel.
⇒ Rp' = 6/3 = 2Ω
⊕ Between X and B :
(1) Rp' and 2Ω are connected in series.
⇒ Rs = 2 + 2 = 4Ω
(2) 2 Ω and 4 Ω are connected in parallel.
⇒ Rp'' = 4/3 Ω
Now,
(3) Rp' and Rs are connected in parallel.
⇒ 1 / Rp"' = 1 / Rs + 1 /Rp'' = 1/4 + 3/4 = 1 Ω
(4) Rp and Rp"' are connected in series.
Rs' = 5+ 1 = 6Ω
(5) Rs' and 6 Ω are in parallel.
R net = 6/2= 3Ω
The equivalent resistance between A and B is 3Ω.
