Answer: R = 394.36ohm
Explanation: In a LR circuit, voltage for a resistor in function of time is given by:
![V(t) = \epsilon. e^{-t.\frac{L}{R} }](https://tex.z-dn.net/?f=V%28t%29%20%3D%20%5Cepsilon.%20e%5E%7B-t.%5Cfrac%7BL%7D%7BR%7D%20%7D)
ε is emf
L is indutance of inductor
R is resistance of resistor
After 4s, emf = 0.8*19, so:
![0.8*19 = 19. e^{-4.\frac{22}{R} }](https://tex.z-dn.net/?f=0.8%2A19%20%3D%2019.%20e%5E%7B-4.%5Cfrac%7B22%7D%7BR%7D%20%7D)
![0.8 = e^{-\frac{88}{R} }](https://tex.z-dn.net/?f=0.8%20%3D%20e%5E%7B-%5Cfrac%7B88%7D%7BR%7D%20%7D)
![ln(0.8) = ln(e^{-\frac{88}{R} })](https://tex.z-dn.net/?f=ln%280.8%29%20%3D%20ln%28e%5E%7B-%5Cfrac%7B88%7D%7BR%7D%20%7D%29)
![ln(0.8) = -\frac{88}{R}](https://tex.z-dn.net/?f=ln%280.8%29%20%3D%20-%5Cfrac%7B88%7D%7BR%7D)
![R = -\frac{88}{ln(0.8)}](https://tex.z-dn.net/?f=R%20%3D%20-%5Cfrac%7B88%7D%7Bln%280.8%29%7D)
R = 394.36
In this LR circuit, the resistance of the resistor is 394.36ohms.
To find a general equilibrium point for a spring based on the hook law, it is possible to start from the following premise:
Hook's law is given by:
![F = k\Delta X](https://tex.z-dn.net/?f=F%20%3D%20k%5CDelta%20X)
Where,
k= Spring Constant
Change in Length
F = Force
When there is a Mass we have two force acting at the System:
W= mg
Where W is the force product of the weigth. Then the force net can be defined as,
![F_{net} = F+W](https://tex.z-dn.net/?f=F_%7Bnet%7D%20%3D%20F%2BW)
But we have a system in equilibrium, so
![0 = K\Delta X -mg](https://tex.z-dn.net/?f=0%20%3D%20K%5CDelta%20X%20-mg)
We find the equilibrium for any location when
![\Delta X = \frac{mg}{k}](https://tex.z-dn.net/?f=%5CDelta%20X%20%3D%20%5Cfrac%7Bmg%7D%7Bk%7D)
Answer:
A lone neutron spontaneously decays into a proton plus an electron.
Explanation:
In an atom, nuclei contain protons and neutrons, which are the fundamental particles of an atom. Neutrons are stable and uncharged particles inside a nucleus.
For 15 times during its lifetime, a free neutron decays and breaks down into more smaller particles.This breakdown causes problems in nuclear reactors, as they start decaying and emit radiations of different wavelengths.
A neutron undergoes the decaying process to produce an electron, a proton, and energy.
The reaction of neutron decay:
n0 → p+ + e− + νe
Answer:
Regions near rivers have water surfaces that rapidly change in temperature from cold to hot.
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