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Question

Say switches S1,S2 and so on upto S6 are closed, one after other in order (first S1, then S2) at regular intervals of 1 minute starting from t=0. The switch S1 is closed at t=1 min. The graph of current versus time is best represented as

A
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B
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C
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D
None of these
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Solution

The correct option is A
Let V be the potential difference across the battery + its adjacent resistance R combination.
At t=0, all the switches are open i0=V15R+V6R
At t=1 minute, S1 is closed. The current flows through minimum resistant path, therefore
i1=V15R+V5R
Similarly, at t=2 minute, S2 is closed, then
i2=V11R+V5R
and so on.
The current increases as the equivalent resistance decreases with every time interval of 1 minute.
After 5 mins, the effective resistance is R and the current will remain constant after that.
Here V is not constant though, since current changes after each minute.
Alternatively, you can find Req for each case and comment on current.
Option (a) is correct.

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