a metallic wire of resistance R is cut into 10 equal pieces. 2 pieces are joined in series and 5 such combinations are joined in parallel. What will be the effective resistance of the combination
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Answer:
The resistance of a conductor is directly proportional to the length of the conductor. The resistance of the metallic wire, when it is cut into ten parts of equal length is r=
10
R
Two such pieces when joined in series, the equivalent resistance of these two parts
=r+r=2r=
10
2R
.
Series resistance of two parts =2X
10
R
=
5
′
R
5 such elements are connected in parallel. Therefore the total resistance R
′
will be
R
′
1
=
R
1
+
R
1
+
R
1
+
R
1
+
R
1
=
R
25
Hence R
′
=
25
R
.
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