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Question

Two identical cycle wheels (geometrically) have a different number of spokes connected from centre to rim. One is having 20 spokes and other having only 10(the rim and the spokes are resistance-less). One resistance of value R is connected between centre and rim. The current in R will be:

A
Double in first wheel than in the second wheel
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B
Four times in first wheel than in the second wheel
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C
Will be double in second wheel than that of the first wheel
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D
Will be equal in both these wheels
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Solution

The correct option is D Will be equal in both these wheels
Since the all the spokes are of same resistance R. And all are parallel connected in the wheel.
( In the figure it is clear).
If n number of spokes are connected in parallel, its equivalent resistance is=$R/n$
The 1st wheel has 20 spokes of resistance R of each.
Equiv. resistance R= R20
If V be the potential difference applied across the wheel,
Current I= V(R10)
I20=VR----- (1)
2nd wheel has 10 spokes,
So, equiv. resistance= R10
Current, I= V(R10)

I10=VR--------- (2)

From the above equations (1) and (2)
I20=VR=I10
Hence the current in R for both wheel is equal.



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