Electrostatics Question 286
Question: A 4 mF capacitor, a resistance of 2.5 MW is in series with 12 V battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given ln(2)= 0.693] [IIT-JEE (Screening) 2005]
Options:
A) 200 and 180 V
B) 180 and 135 V
C) 160 and 80 V
D) 140 and 20 V
Show Answer
Answer:
Correct Answer: B
Solution:
$ V=V _{0}({{e}^{-\lambda t}}) $
After 1 seconds $ V _{1}=320({{e}^{-\lambda }})\Rightarrow 240=320({{e}^{-\lambda }})\Rightarrow {{e}^{-\lambda }}=\frac{3}{4} $
After 2 seconds $ V _{2}=320{{({{e}^{-\lambda }})}^{2}}=320\times {{( \frac{3}{4} )}^{2}}=180volt $
After 3 seconds $ V _{3}=320{{({{e}^{-\lambda }})}^{3}}=320\times {{( \frac{3}{4} )}^{3}}=135volt $
