The voltage across a 5-μF capacitor is known to be vc = 125t e^(−1000t) V for t ≥ 0.
(a) Find the current through the capacitor for t > 0. Assume the passive sign convention.
(b) Find the power at the terminals of the capacitor when t = 15 μs.
(c) Is the capacitor absorbing or delivering power at t = 15 μs?
(d) Find the energy stored in the capacitor at t = 15μs.

a) i(t)=2.5*(e^(-2500*t))*(1-2500*t) mA

b) P=16.7 μW

c) the capacitor is absorbing power.

d) E = 1.29x10^-10 nJ

Explanation:

In this exercise we will use the concepts and formulas of electric current. The step-by-step solution is seen in the attached image.

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.