How many time constants must elapse if an initially charged capacitor is to discharge 90% of its stored energy through a resistor

t = log9/10 x RC

Explanation:

Let's say initial energy is

E= 1/2Q²/C

But if 90% is discharged what will be remaining will be

E= E"/100= 1/2Q²/C

So if we divide the first by the second equation we have

Q'= Q/10

Then using

q=q0(1-e^-t /RC)

So that

Q= Q/10(1-e^-t /RC)

t/RC= log9/10

So t = log9/10 x RC

it would be c. predictability

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.