Home
Class 12
PHYSICS
A capacitor of capacity 0.1 muF connecte...

A capacitor of capacity `0.1 muF` connected in series to a resistor of `10 M Omega` is charged to a certain potential and then made to discharge through resistor. The time in which the potential will take to fall to half its original value is (Given, `log_(10) 2 = 0.3010`)

A

`2 s`

B

`0.693 s`

C

`0.5 s`

D

`1.0 s`

Text Solution

Verified by Experts

The correct Answer is:
B
By equation of charging,
`q = q_(0)(1 - e^(-t//CR))`
According to question,
`(q)/(q_(0)) = (1)/(2) = 0.50 :. 0.50 = 1 - e^(-t//CR)`
`e^(-t//CR) = 1 - 0.50 = 0.50 rArr e^(t//CR) = 2`
or (t)/(CR) = log_(e)2 or (t)/(CR) = 2.3026 log_(10)2`
or `t = CRxx2.3026log_(10)2`
or `t = 0.1xx10^(-6)xx10xx10^(6)xx2.3026 log_(10)2`
or `t = 2.3026xx0.3010 or t = 0.693 s`
Promotional Banner

Topper's Solved these Questions

  • ELECTRIC CAPACITOR

    BITSAT GUIDE|Exercise BITSAT archives|6 Videos

  • CURRENT ELECTRICITY

    BITSAT GUIDE|Exercise Bitsat Archives|26 Videos

  • ELECTRIC CHARGE

    BITSAT GUIDE|Exercise All Questions|28 Videos

Similar Questions

Explore conceptually related problems

A capacitor of capacitance 0.1 muF is charged to a certain potential through resistance of 10 M Omega and then discharged. Calculate the time in which the potential will fall to half its original value.

A capacitor is charged and then made to discharged through a resistance. The time constant is tau . In what time will the potential difference across the capacitor decreases by 10% ?

Three capacitors of capacitacnce 1.0, 2.0 and 5.0muF are connected in series to a 10 V source. The potential difference across the 2.0muF capacitor is

Three capacitors of 2.0, 3.0 and 6.0 muF are connected in series to a 10 V source. The charge on the 3.0 muF capacitor is

A capacitor of 20muF charged upto 500 V is connected in parallel with another capacitor of 10muF , which is charged upto 200 V. the common potential is

An uncharged capacitor is connected in series with a resistor and a battery. The charging of the capacitor starts at t=0. The rate at which energy stored in the capacitor:-

Two capacitors of 1muF and 2muF are connected in series and this combination is charged upto a potential difference of 120 volt. What will be the potential difference across 1 micro farad capacitor ?