Current Electricity Charging Discharging Of Capacitors Question 133
Question: Two uniform wires $ A $ and $ B $ are of the same metal and have equal masses. The radius of wire $ A $ is twice that of wire $ B $ . The total resistance of A and $ B $ when connected in parallel is
[MNR 1994]
Options:
A) $ 4,\Omega $ when the resistance of wire $ A $ is $ 4.25,\Omega $
B) $ 5,\Omega $ when the resistance of wire $ A $ is $ 4.25,\Omega $
C) $ 4,\Omega $ when the resistance of wire $ B $ is $ 4.25,\Omega $
D) $ 4,\Omega $ when the resistance of wire $ B $ is $ 4.25,\Omega $
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Answer:
Correct Answer: A
Solution:
$ \frac{R _{A}}{R _{B}}={{( \frac{r _{B}}{r _{A}} )}^{4}} $
Therefore $ \frac{R _{A}}{R _{B}}={{( \frac{1}{2} )}^{4}}=\frac{1}{16} $
Therefore $ R _{B}=16R _{A} $ When RA and RB are connected in parallel then equivalent resistance $ R _{eq}=\frac{R _{A}R _{B}}{(R _{A}+R _{B})}=\frac{16}{17}R _{A} $ If $ R _{A}=4.25\Omega $ then $ R _{eq}=4\Omega $ i.e. option is correct.
BETA
