Electrostatics Question 282
Question: The plates of a capacitor are charged to a potential difference of 320 volts and are then connected across a resistor. The potential difference across the capacitor decays exponentially with time. After 1 second the potential difference between the plates of the capacitor is 240 volts, then after 2 and 3 seconds the potential difference between the plates will be [MP PET 1996]
Options:
A) With $ S _{1} $ closed, $ V _{1}=15V,\ V _{2}=20\ V $
B) With $ S _{3} $ closed $ V _{1}=V _{2}=25V $
C) With $ S _{1} $ and $ S _{2} $ closed $ V _{1}=V _{2}=0 $
D) With$ S _{1} $ and $ S _{3} $ closed, $ V _{1}=30V,\ V _{2}=20V $
Show Answer
Answer:
Correct Answer: D
Solution:
Charges on capacitors are $ Q _{1}=30\times 2=6pC $
and $ Q _{2}=20\times 3=60pC $ or $ Q _{1}=Q _{2}=Q(\text{say}) $
The situation is situation is similar as the two capacitors in series are first charged with a battery of emf 50 V and then disconnected \ when $ {S _{\text{3}}} $
is closed $ V _{1}=30V $ and $ V _{2}=20V $
