Current Electricity Charging Discharging Of Capacitors Question 672
A battery of emf $ E _{0}=12,V $ is connected across a 4 m long uniform wire having resistance $ \frac{4\Omega }{m} $ the cells of small emfs $ {\varepsilon _{1}}=2,V $ and $ {\varepsilon _{2}}=4,V $ having internal resistance 2 $ \Omega $ and 6 $ \Omega $ respectively, are connected as shown in the figure. If galvan,ometer shows no deflection at the point N, the distance of point N from the point A is equal to
Options:
A) $ \frac{1}{6}m $
B) $ \frac{1}{3}m $
C) $ 25m $
D) $ 50m $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Potential gradient $ x=( \frac{12}{8+16} )\times 4=2V{{m}^{-1}} $ Effective emf of $ E _{1} $ and $ E _{2} $
$ E=\frac{\frac{E _{2}}{r _{2}}-\frac{E _{2}}{r _{1}}}{1/r _{1}+1/r _{2}}=\frac{1}{2}volt $ Balancing length $ =( \frac{1}{2} )( r _{1}+r _{2} )=\frac{1}{4}m=25cm $
BETA
