Answer:
parallel circuit
Explanation:
In a parallel circuit, the potential difference across each of the resistors that make up the circuit is the same. This leads to a higher current flowing through each resistor and subsequently the total current flowing through all the resistors is higher.
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mass gram, time sec, temp kelvin, vol liter, dens grams/cm3
85 N - 40 N = 45 N
And depending on direction the greater force is being pulled towards
Answer:
The curl is ![0 \hat x -z^2 \hat y -4xy \hat z](https://tex.z-dn.net/?f=0%20%5Chat%20x%20-z%5E2%20%5Chat%20y%20-4xy%20%5Chat%20z)
Explanation:
Given the vector function
![\vec A (\vec r) =4x^3 \hat{x}-2x^2y \hat y+xz^2 \hat z](https://tex.z-dn.net/?f=%5Cvec%20A%20%28%5Cvec%20r%29%20%3D4x%5E3%20%5Chat%7Bx%7D-2x%5E2y%20%5Chat%20y%2Bxz%5E2%20%5Chat%20z)
We can calculate the curl using the definition
![\nabla \times \vec A (\vec r ) = \left|\begin{array}{ccc}\hat x&\hat y&\hat z\\\partial/\partial x&\partial/\partial y&\partial/\partial z\\A_x&X_y&A_z\end{array}\right|](https://tex.z-dn.net/?f=%5Cnabla%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%20%3D%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%20x%26%5Chat%20y%26%5Chat%20z%5C%5C%5Cpartial%2F%5Cpartial%20x%26%5Cpartial%2F%5Cpartial%20y%26%5Cpartial%2F%5Cpartial%20z%5C%5CA_x%26X_y%26A_z%5Cend%7Barray%7D%5Cright%7C)
Thus for the exercise we will have
![\nabla \times \vec A (\vec r ) = \left|\begin{array}{ccc}\hat x&\hat y&\hat z\\\partial/\partial x&\partial/\partial y&\partial/\partial z\\4x^3&-2x^2y&xz^2\end{array}\right|](https://tex.z-dn.net/?f=%5Cnabla%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%20%3D%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%20x%26%5Chat%20y%26%5Chat%20z%5C%5C%5Cpartial%2F%5Cpartial%20x%26%5Cpartial%2F%5Cpartial%20y%26%5Cpartial%2F%5Cpartial%20z%5C%5C4x%5E3%26-2x%5E2y%26xz%5E2%5Cend%7Barray%7D%5Cright%7C)
So we will get
![\nabla \times \vec A (\vec r )= \left( \cfrac{\partial}{\partial y}(xz^2)-\cfrac{\partial}{\partial z}(-2x^2y)\right) \hat x - \left(\cfrac{\partial}{\partial x}(xz^2)-\cfrac{\partial}{\partial z}(4x^3) \right) \hat y + \left(\cfrac{\partial}{\partial x}(-2x^2y)-\cfrac{\partial}{\partial y}(4x^3) \right) \hat z](https://tex.z-dn.net/?f=%5Cnabla%20%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%3D%20%5Cleft%28%20%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7D%28xz%5E2%29-%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20z%7D%28-2x%5E2y%29%5Cright%29%20%5Chat%20x%20-%20%5Cleft%28%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20x%7D%28xz%5E2%29-%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20z%7D%284x%5E3%29%20%5Cright%29%20%5Chat%20y%20%2B%20%5Cleft%28%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20x%7D%28-2x%5E2y%29-%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7D%284x%5E3%29%20%5Cright%29%20%5Chat%20z)
Working with the partial derivatives we get the curl
![\nabla \times \vec A (\vec r )=0 \hat x -z^2 \hat y -4xy \hat z](https://tex.z-dn.net/?f=%5Cnabla%20%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%3D0%20%5Chat%20x%20-z%5E2%20%5Chat%20y%20-4xy%20%5Chat%20z)