Current Electricity Charging Discharging Of Capacitors Question 514
Question: Two wires ‘A’ and ‘B’ of the same material have their lengths in the ratio 1 : 2 and radii in the ratio 2 : 1. The two wires are connected in parallel across a battery. The ratio of the heat produced in ?A? to the heat produced in ?B? for the same time is
[MNR 1998]
Options:
A) $ 1:2 $
B) $ 2:1 $
C) $ 1:8 $
D) $ 8:1 $
Show Answer
Answer:
Correct Answer: D
Solution:
$ R _{1}=\rho \frac{l _{1}}{A _{1}} $ and $ R _{2}=\rho \frac{l _{2}}{A _{2}} $
Therefore $ ,\frac{R _{1}}{R _{2}}=\frac{l _{1}}{l _{2}}.\frac{A _{2}}{A _{1}}=\frac{l _{1}}{l _{2}}{{( \frac{r _{2}}{r _{1}} )}^{2}} $ Given $ \frac{l _{1}}{l _{2}}=\frac{1}{2} $ and $ \frac{r _{1}}{r _{2}}=\frac{2}{1} $ or $ \frac{r _{2}}{r _{1}}=\frac{1}{2} $
Therefore $ \frac{R _{1}}{R _{2}}=\frac{1}{8} $
$ \
Therefore $ Ratio of heats $ \frac{H _{1}}{H _{2}}=\frac{V^{2}/R _{1}}{V^{2}/R _{2}}=\frac{R _{2}}{R _{1}}=\frac{8}{1} $
BETA
