The question states that the potential difference dropped from  to  in . The percentage of voltage drop is:

This means that there was a  voltage drop in . The definition of time constant is the time it takes for a capacitor to discharge to of its original value, or have a  drop; therefore, the time constant for this circuit is .

The time constant, tau, for an RC circuit is the product of the resistance of the resistor and the capacitance of the capacitor:

We can use this equation to solve for the resistance of the resistor:

Solving for resistance gives us:

Notice that you could have used the voltage decay equation to solve this problem; however, knowing the definition of time constant simplifies the problem and reduces the amount of calculations.

The equation for resistance is given by .

From this equation, we can see the best way to decrease resistance is by increasing the cross-sectional area, , of the cord. Increasing the length, , of the cord or the resistivity, , will increase the resistance.  

To relate resistance R, resistivity , area A, and length L we use the equation.

Rearranging to isolate the quantity we wish to solve for, L, gives the equation . We must first solve for A using the radius, 0.725mm.

Plugging in our numbers gives the answer, 960m.

Resistors in serries add according to the formula:

Resistors in parallel add according to the formula:

We can find the total equivalent resistance:

Now we can use Ohm's law to find the current:

Solve: 

To find resistance from voltage and current, we will need to use Ohm's law:

We are given the voltage and current, allowing us to solve for the resistance.

The atomic mass of an element is determined by the proportional mass of each elemental isotope. We know that there are only two isotopes of lithium; therefore, their percentages must add to 100%.

The atomic mass will be equal to the mass of each isotope multiplied by its abundance.

We can substitute an algebraic expression to solve for one of our variables.

Using this value, we can solve for the abundance of the other isotope.

Converting these values to percentages gives us our final answer.

It is important to remember that one mole of an element contains 6.022 * 10²³ atoms. Since there are two moles of carbon dioxide (CO₂), we can conclude that there are two moles of carbon. As a result, there are  atoms.

A mole is defined as the number of atoms present in  of carbon-12. Obtaining a sample of carbon-12 will give you  of carbon-12. You can also find the number of moles by multiplying the mass by the molecular weight of carbon:

Remember that a mole of any element contains  atoms (Avogadro’s number). Since we have exactly one mole in the sample, there will be exactly  atoms of carbon-12.

Remember that the empirical formula relies on the ratio of the moles of elements. To get the number of atoms, you would have to multiply the moles of each element by the Avogadro’s number (). You would use this number for every element (Avogadro’s number doesn’t change for each element). This means that the ratio of the number of atoms will be the same as the ratio of the number of moles, and you will get the same empirical formula. There is a constant relationship between the number of moles and the number of atoms in a sample.

Each answer choice is presented in grams. To convert to moles, we will need to divide each choice by the atomic mass of the presented element.

Two grams of hydrogen atoms will result in the greatest amount of moles.