Capacitor


After 2.3 time constant does the energy of capacitor becomes 1/10 of its initial value
Explanation :
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