Current Electricity Charging Discharging Of Capacitors Question 131
Question: For ensuring dissipation of same energy in all three resistors $ (R _{1},,R _{2},,R _{3}) $ connected as shown in figure, their values must be related as ]
[AIIMS 2005]
Options:
A) $ R _{1}=R _{2}=R _{3} $
B) $ R _{2}=R _{3} $ and $ R _{1}=4R _{2} $
C) $ R _{2}=R _{3} $ and $ R _{1}=\frac{1}{4}R _{2} $
D) $ R _{1}=R _{2}+R _{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
As the voltage in $ R _{2} $ and $ R _{3} $ is same therefore, according to, $ H=\frac{V^{2}}{R}.t, $
$ R _{2}=R _{3} $ Also the energy in all resistance is same. \ $ i^{2}R _{1}t=i _{1}^{2}R _{2}t $ Using $ i _{1}=\frac{R _{3}}{R _{2}+R _{3}}i=\frac{R _{3}}{R _{3}+R _{3}}i=\frac{1}{2}i $ Thus $ i^{2}R _{1}t=\frac{i^{2}}{4}R _{2}t $ or, $ R _{1}=\frac{R _{2}}{4} $
BETA
