Two capacitors with capacitances of 1.0 m F and 0.50 m F, respectively, are connected in series. The system is connected to a 100-V battery. What electrical potential energy is stored in the 1.0- m F capacitor?

The energy stored in the 1.0mF capacitor is 9.0*10^-5J

Data given;

Since the capacitor are in series, the total capacitance is;

substitute in the values and solve.

The capacitance in the capacitor is 3mF.

This is the energy stored in the capacitor.

U = potential energy

q = charge

C = capacitor.

But the charge of a capacitor is given as

The charge on the capacitor is 0.3C

We can proceed to use this formula and solve for the potential energy stored in the 1.0mF capacitor.

From the calculations above, the potential energy stored in the 1mF capacitor is .

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Therefore energy is stored in the 1.0 mF capacitor is 5.56×10⁻⁹ J

Explanation:

Series capacitor: The ending point of a capacitor is the starting point of other capacitor.

If C₁ and C₂ are connected in series then the equivalent  capacitance is C.

where    

Given that,

C₁ = 1.0 mF=1.0×10⁻³F  and  C₂ = 0.50mF=0.50×10⁻³F  

If C is equivalent capacitance.

Then    

mF

Again given that the system is connected to a 100-v battery.

We know that

q=Cv

q= charge

C= capacitor

v= potential difference

Therefore

The electrical potential energy stored in a capacitor can be expressed

q= charge

c=capacitance of a capacitor

Therefore energy is stored in the 1.0 mF capacitor is

J

momentum of soft ball three times less than baskey ball

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.