The correct option is
A No change in the value of current passing through resistance
ALet us assign same electric potential to the points connected through same conducting wire in the given circuit.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1237214/original_40.1.png)
Now redrawing the circuit, when switch
S is open.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1237232/original_40.2.png)
Due to switch
S in open condition the resistance in that branch will vanish. Thus, there are effectively three resistances with value
r connected in parallel between points
1 and
2.
⇒Req=r3
The current supplied by battery in the circuit will be,
i1=E(r3)=3Er
Since all the three resistances are identical, therefore current will get distributed equally in each of them.
Hence current through resistor
A,
iA=i13=Er
After the switch
S is closed:
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1237207/original_40.3.png)
We can observe that there are effectively four resistances with value
r connected in parallel between points
1 and
2.
⇒Req=r4
The current supplied by battery in the circuit will be,
i2=E(r4)=4Er
Since all the four resistances are identical, therefore current will get distributed equally in each of them.
Hence current through resistor
A,
iA=i24=(4Er)4=Er
⇒The value of current through resistor
A will remain the same.
Why this question?
Tip––––:In such problems always focus on obtaining a simple circuit by using point potential technique.
The current will not flow in a branch in which the electrical path is broken, thus resistance in such paths can be neglected.
Caution:––––––––––In this question, the value of current through resistance A has not changed due to identical resistance. However the current in circuit will increase after switch S closed because Req↓ for the circuit. |