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

Answer 1

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 $R$= $\frac{R}{20}$

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)

2nd 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.