What fraction of the final energy is stored in an initially uncharged capacitor

Question

What fraction of the final energy is stored in an initially uncharged capacitor after is has been charged for 2.3 times constants? a. 0.50 b. 0.60 c. 0.75 d. 0.81 e. 0.90 Three massive charged balls are as shown in the figure below. A frictionless rod running along the x axis constrains the motion of Bell 3 to 3 slide along this axis. Ball 1 and Ball 2 are fixed on the y axis at + 4.0 cm, respectively Ball 3 is initially located at x = 8.0 cm and is held fixed. Imagine releasing Ball 3 from rest remember, it can only move along the x axis). Ball 3 will a. Eventually come to rest at the origin b. oscillate back and forth along the x axis about the origin c. Fly off to negative infinity along the x axis d. Fly off to positive infinity along the x axis A circular coil (radius R = 0.40 m) has 160 turns and is a uniform magnetic field. If the in the orientation of the coil is varied through all possible positions, the maximum torque on coil by magnetic forces is 0.16 Nm when the current in the coil is 4.0 mA. What is magnitude of the magnetic field? a. 1.0 T b. 0.75 T c. 0.5 T d. 0.25 T e. 0.125 T

Explanation / Answer

in the charging condition,charge on plates of capacitor after t sec is q = Q*(1-e^(-t/T))

T is the time constant

given that t = 2.3 T

then q = Q*(1-e^(-2.3T/T))

q = Q*(1-e^(-2.3)) = 0.899Q

energy stored after 2.3 time constants is U1 = q^2/(2*C) = 0.899^2*Q^2/(2C) = 0.81*Q^2/(2C)

final energy stored is U = Q^2/2C

then required fraction is U1/U = 0.81

so the answer is D) 0.81

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