Question

A charged capacitor is connected with a resistor. After how many time constants, does the energy of capacitor become 1/10th of it's initial value ​

Answer 1

Answer:hiii friend here is you correct answer

after 2.3 time constant does the energy of capacitor becomes 1/10 of its initial value

The discharging equation of a capacitor is given by,

Q = Q₀e^(-t/T)

where,

Q₀ = initial charge

T = Time constant

Q = charge at time t = Q₀/10

putting these values in the above equation we get,

Q₀/10 = Q₀e^(-t/T)

=> e^(-t/T) = 1/10 = 0.1

taking log on both the sides

lne^(-t/T) = ln 0.1

=> (-t/T) = -2.3

=> t = 2.3T

Hence after 2.3  time constant does the energy of capacitor becomes 1/10 of its initial value

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