Current Electricity Charging Discharging Of Capacitors Question 680
In the network shown, each resistance is equal to R. The equivalent resistance between adjacent corners A and D is
Options:
A) $ R $
B) $ \frac{2}{3}R $
C) $ \frac{3}{7}R $
D) $ \frac{8}{15}R $
Show Answer
Answer:
Correct Answer: D
Solution:
The equivalent circuit is as shown in figure. The resistance of arm AOD (=R+R) is in parallel to the resistance R of arm AD. Their effective resistance $ R _{1}=\frac{2R\times R}{2R+R}=\frac{2}{3}R $ The resistance of arms AB, BC and CD is $ R _{2}=R+\frac{2}{3}R+R=\frac{8}{3}R $ The resistance $ R _{1} $ and $ R _{2} $ are in parallel. The effective resistance between A and D is $ R _{3}=\frac{R _{1}\times R _{2}}{R _{1}+R _{2}}=\frac{\frac{2}{3}R\times \frac{8}{3}R}{\frac{2}{3}R+\frac{8}{3}R}=\frac{8}{15}R $
BETA
