Current Electricity Charging Discharging Of Capacitors Question 382
Question: Two wires A and B of same material and same mass have radius 2rand r. If resistance of wire A is $ 34,\Omega $ , then resistance of B will be
[RPET 1997]
Options:
A) $ 544,\Omega $
B) $ 272,\Omega $
C) $ 68,\Omega $
D) $ 17,\Omega $
Show Answer
Answer:
Correct Answer: A
Solution:
$ R=\rho \frac{l}{A} $ and mass m = volume (V) ´ density = (A l) d Since wires have same material so r and d is same for both. Also they have same mass
Therefore Al = constant
Therefore $ l\propto \frac{1}{A} $
Therefore $ \frac{R _{1}}{R _{2}}=\frac{l _{1}}{l _{2}}\times \frac{A _{2}}{A _{1}}={{( \frac{A _{2}}{A _{1}} )}^{2}}={{( \frac{r _{2}}{r _{1}} )}^{4}} $
Therefore $ \frac{34}{R _{2}}={{( \frac{r}{2r} )}^{4}} $
Therefore $ R _{2}=544,\Omega $
BETA
