Current Electricity Charging Discharging Of Capacitors Question 683
Question: The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then
Options:
A) the resistance and the specific resistance, will both remain unchanged
B) the resistance will be doubled and the specific resistance will be halved
C) the resistance will be halved and the specific resistance will be remain unchanged
D) the resistance will be halved and the specific resistance will be doubled
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ R=\frac{\rho {\ell _{I}}}{A _{1}}, $ now $ {\ell _{2}}=2{\ell _{1}} $
$ A _{2}=\pi {{( r _{2} )}^{2}}=\pi {{( 2r _{1} )}^{2}}=4\pi r _{1}^{2}=4A _{1} $
$ \
Therefore R _{2}=\frac{\rho ( 2{\ell _{1}} )}{4A _{1}}=\frac{\rho ,\ell }{2A}=\frac{R}{2} $
$ \
Therefore $ Resistance is halved, but specific resistance remains the same.
BETA
