Question

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

• A. double in the first wheel than in the second wheel
• B. four times in the first wheel than in the second wheel
• C. wiil be double in the second wheel than that of the first wheel
• D. will be equal in both these wheels

Answer 1

Answer: (D)

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 $1$ st wheel has $20$ spokes of resistance $R$ of each.
Equiv. resistance $R=\frac{R}{20}$
If $V$ be the potential difference applied across the wheel,
Current $I =\frac{ V }{\left(\frac{ R }{10}\right)} $
$\frac{ I }{20}=\frac{ V }{ R }\,\,\,\, ...(1)$
$2$nd wheel has $10$ spokes,
So, equiv. resistance $=\frac{R}{10}$
Current, $I =\frac{ V }{\left(\frac{ R }{10}\right)}$
$\frac{I}{10}=\frac{V}{R}\,\,\, ...(2)$
From the above equations (1) and (2)
$\frac{ I }{20}=\frac{ V }{ R }=\frac{ I }{10}$
Hence the current in $R$ for both wheel is equal.