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Question

In the circuit shown in figure, after closing the switch S, what is the change in current flowing through the resistance A?


A
No change in the value of current passing through resistance A
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B
The current passing through resistance A decreases
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C
The current passing through resistance A increases
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D
Data is insufficient to say anything
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Solution

The correct option is A No change in the value of current passing through resistance A
Let us assign same electric potential to the points connected through same conducting wire in the given circuit.


Now redrawing the circuit, when switch S is open.


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:


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.

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