Five identical resistance wires of $ 1 \Omega $ each, are connected as shown in the figure as clear lines. If two similar wires are added as shown by dashed lines, find the change in resistance between A & F : (1) $ 2 \Omega $ (2)$ 1 \Omega $ (3)$ 3 \Omega $ (4) $ 4 \Omega $
Here, in the given problem, initially, 5 resistances are in series so equivalent resistance is ${R}_{i}=5R$
When we add two more resistances, BCED will make a balanced Wheatstone bridge circuit. So there is no current through resistance in between C and D and it is removed from the circuit and the corresponding circuit is redrawn as shown in the figure.
The equivalent resistance for the Wheatstone bridge is ${R}_{be}=(1+1)||(1+1)=2||2=\frac{2\times 2}{2+2}=1\Omega $
Final resistance of the whole circuit is ${R}_{f}={R}_{ab}+{R}_{be}+{R}_{ef}=1+1+1=3\Omega $
Charge in resistance $={R}_{i}-{R}_{f}=5-3=2\Omega $
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
"
