Question
Four wires each of the same length, diameter and material are connected to form a square. If the resistance of each wire is R, then equivalent resistance across the opposite corners is :
Answer: Option A
:
A
The connection of wires is as shown below.
We have to calculate equivalent resistance across the opposite corners i.e. across A and D or B and C. If we take two corners B and C, then we can clearly see that the resistances of AB and AC, and CD and BD are in series.
So the equivalent resistance across CAB is 2R ( CA and AB are in series) and CDB is also 2R ( CD and BD are in series).
The two equivalent resistances across CAB and CDB are in parallel. Hence, the equivalent resistance across the two corners i.e. B and C is 1Req=12R+12R.
On solving we get, Req=R. Similarly, equivalent resistance across A and D will also be R.
Hence the equivalent resistance across the opposite corners is R.
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:
A
The connection of wires is as shown below.
We have to calculate equivalent resistance across the opposite corners i.e. across A and D or B and C. If we take two corners B and C, then we can clearly see that the resistances of AB and AC, and CD and BD are in series.So the equivalent resistance across CAB is 2R ( CA and AB are in series) and CDB is also 2R ( CD and BD are in series).
The two equivalent resistances across CAB and CDB are in parallel. Hence, the equivalent resistance across the two corners i.e. B and C is 1Req=12R+12R.
On solving we get, Req=R. Similarly, equivalent resistance across A and D will also be R.
Hence the equivalent resistance across the opposite corners is R.
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