Electro Magnetic Induction And Alternating Currents Question 181
Question: The two capacitors, shown in the circuit, are initially uncharged and the cell is ideal. The switch S is closed at t=0. Which of the following functions represents the current i(t) through the cell as a function of time? Here $ i_{0},,i_{1},,i_{2} $ are constants.
Options:
A) $ i(t)=i_{0}+i_{1}{{e}^{-t/\tau }} $ ; $ \tau =3C\times \frac{R}{3} $
B) $ i(t)=i_{0}+i_{1}{{e}^{-t/\tau }}+i_{2}{{e}^{-t/2\tau }} $ ; $ \tau =RC $
C) $ i(t)=i_{1}+i_{1}{{e}^{-t/\tau }} $ ; $ \tau =3C\times \frac{R}{3} $
D) $ i(t)=i_{0}+i_{1}{{e}^{-t/\tau }} $ ; $ \tau =3RC $
Show Answer
Answer:
Correct Answer: B
Solution:
- The three branches of the circuits carry currents $ i=i_{0} $ , $ i=i_{1},{{e}^{t/RC}} $ and $ i=i_{2},2{{e}^{-t/2Rc}} $ respectively. The current through the cell, i(t) can be found by using Kirchhoff’s current law (or mode law).
