Answer:
The resistance must be 6.67![\Omega](https://tex.z-dn.net/?f=%5COmega)
Solution:
Resistance, ![R_{1} = 20\Omega](https://tex.z-dn.net/?f=R_%7B1%7D%20%3D%2020%5COmega)
Resistance, ![R_{2} = 10\Omega](https://tex.z-dn.net/?f=R_%7B2%7D%20%3D%2010%5COmega)
For the current to be the same when the switch is open or closed, the resistances must be connected in parallel as current is distributed in parallel with the same voltage across the circuit:
Thus in parallel:
![\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7BR_%7Beq%7D%7D%20%3D%20%5Cfrac%7B1%7D%7BR_%7B1%7D%7D%20%2B%20%5Cfrac%7B1%7D%7BR_%7B2%7D%7D)
![\frac{1}{R_{eq}} = \frac{1}{20} + \frac{1}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7BR_%7Beq%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B20%7D%20%2B%20%5Cfrac%7B1%7D%7B10%7D)
![R_{eq} = 6.67\ \Omega](https://tex.z-dn.net/?f=R_%7Beq%7D%20%3D%206.67%5C%20%5COmega)
I believe the answer is "When a neutral atom looses an electron to another neutral atom, two charged atoms are created."
Answer:
L = μ₀ n r / 2I
Explanation:
This exercise we must relate several equations, let's start writing the voltage in a coil
= - L dI / dt
Let's use Faraday's law
E = - d Ф_B / dt
in the case of the coil this voltage is the same, so we can equal the two relationships
- d Ф_B / dt = - L dI / dt
The magnetic flux is the sum of the flux in each turn, if there are n turns in the coil
n d Ф_B = L dI
we can remove the differentials
n Ф_B = L I
magnetic flux is defined by
Ф_B = B . A
in this case the direction of the magnetic field is along the coil and the normal direction to the area as well, therefore the scalar product is reduced to the algebraic product
n B A = L I
the loop area is
A = π R²
we substitute
n B π R² = L I (1)
To find the magnetic field in the coil let's use Ampere's law
∫ B. ds = μ₀ I
where B is the magnetic field and s is the current circulation, in the coil the current circulates along the length of the coil
s = 2π R
we solve
B 2ππ R = μ₀ I
B = μ₀ I / 2πR
we substitute in
n ( μ₀ I / 2πR) π R² = L I
n μ₀ R / 2 = L I
L = μ₀ n r / 2I