metallic wire of length L and cross sectional area A has a resistance R. Two wires of same material length 1/2 and cross sectional area 3A are connected in series. The combination has resistance
of
al R/6
b)R/3
c) 3R
d) 6R
Answers
Answer:
Correct option is B)
Explanation:
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Two metallic wires A and B are connected in series Wire A has length l and radius r while wire B has length 2l and radius 2r If both the wires are of same material then and the ratio of the total resistance of series combination to the resistance of the wire A
Medium
Solution
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Correct option is B)
Let the resistivity of both the wires be 'ρ'.
The resistance of the wire A is given as R
A
=
πr
2
ρl
.
The resistance of the wire B is given as R
B
=
π2r
2
ρ2l
=
2πr
2
ρl
.
Now when the resistance are connected in seires is R=R
A
+R
B
. That is, R=
2
3
(
πr
2
ρl
).
So, the required ratio is R:R
A
=
2
3
(
πr
2
ρl
):
πr
2
ql
.
Therefore, R:R
A
=3:2.
Hence, the ratio of the resistances in series and only wire A is 3/2.