Answer:
Voltage across the capacitor is 30 V and rate of energy across the capacitor is 0.06 W
Explanation:
As we know that the current in the circuit at given instant of time is
i = 2.0 mA
R = 10 k ohm
now we know by ohm's law



so voltage across the capacitor + voltage across resistor = V


Now we know that

here rate of change in energy of the capacitor is given as



Answer:
M₀ = 5i - 4j - k
Explanation:
Using the cross product method, the moment vector(M₀) of a force (F) is about a given point is equal to cross product of the vector A from the point (r) to anywhere on the line of action of the force itself. i.e
M₀ = r x F
From the question,
r = i + j + k
F = 1i + 0j + 5k
Therefore,
M₀ = (i + j + k) x (1i + 0j + 5k)
M₀ = ![\left[\begin{array}{ccc}i&j&k\\1&1&1\\1&0&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C1%261%261%5C%5C1%260%265%5Cend%7Barray%7D%5Cright%5D)
M₀ = i(5 - 0) -j(5 - 1) + k(0 - 1)
M₀ = i(5) - j(4) + k(-1)
M₀ = 5i - 4j - k
Therefore, the moment about the origin O of the force F is
M₀ = 5i - 4j - k
For each pair Independent variable and the dependent variable is -
a. How much gas is left in the gas tank vs. how far the car has traveled.
- Independent variable = how far the car has traveled
- dependent variable = How much gas is left in the gas tank
b. How much money you've spent vs. how much money is in your wallet.
- Independent variable = How much money you've spent
- dependent variable = how much money is in your wallet.
c. How far a toy car traveled vs. how much time went by
- Independent variable = how much time went by
- dependent variable = How far a toy car traveled
An independent variable in any experiment or research is a variable that is manipulated or changed in the experiment, this change leads to a direct effect on the dependent variable.
A dependent variable is a variable that is directly affected by the independent variable and it is the variable that is measured or tested in an experiment.
Thus,
a. How much gas is left in the gas tank vs. how far the car has traveled.
- Independent variable = how far the car has traveled
- dependent variable = How much gas is left in the gas tank
b. How much money you've spent vs. how much money is in your wallet.
- Independent variable = How much money you've spent
- dependent variable = how much money is in your wallet.
c. How far a toy car traveled vs. how much time went by
- Independent variable = how much time went by
- dependent variable = How far a toy car traveled
Learn more about dependent variables:
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