# AP Physics B : Electric Circuits

## Example Questions

### Example Question #1 : Understanding Capacitors

Which of the following is equal to the time constant of an RC circuit?

Explanation:

The definition of a time constant for an RC circuit is the product of resistance and charge:

This is defined as the time it takes the capacitor to reach a charge that is around 63% of the maximum charge. It is also the time it takes to discharge around 37% of the charge. This value is commonly used to determine the amount of charge a capacitor has or the amount of current flowing through the capacitor at any given time point.

### Example Question #1 : Understanding Capacitors

Which of the following statements is false regarding capacitors?

I. A larger capacitor stores more energy

II. Capacitors connected in parallel have the same voltage drop

III. Increasing the distance between the two plates increases the capacitance

III only

I only

I and III

II and III

I and III

Explanation:

Recall the equation for potential energy in terms of capacitance:

According to the equation above, an increase in capacitance will lead to decrease in the amount of energy stored. This means that a larger capacitor will store less energy; therefore, statement I is false.

Any circuit elements connected in parallel will always have the same voltage drop. This applies to resistors, capacitors, and inductors. Statement II is true.

Remember that capacitance is defined as follows:

In this equation, is the area of the plates and  is distance between the plates. Increasing  will lead to a decrease in capacitance; therefore, statement III is false.

### Example Question #1 : Ap Physics 2

A capacitor has a stored charge of  and a potential energy of . What is the voltage across the capacitor?

Explanation:

To solve this problem, you need to use the following two equations:

By substituting into the second equation you can write the change in potential energy in terms of voltage and charge.

Rearranging the previous equation will allow us to solve for the voltage.

Use the given values for stored potential energy and charge to solve for the voltage.

### Example Question #1 : Electric Circuits

battery is hooked to a circuit with a  and a  resistor in series with each other, and with a branched set of three parallel resistors of , , and . What current does this circuit draw from the battery?

Explanation:

Our first step will be to find the equivalent resistance of the circuit. Simple resistors add in series, and add inversely in parallel. For the  and  resistors in series, the total resistance is simply the sum.

For the resistors in parallel, the inverse of the total resistance is equal to the sum of the inverse of the individual resistors.

The total resistance of the circuit will be the sum of the series resistance and parallel resistance.

Now we know the total resistance of the circuit and the voltage supplied from the battery. Use Ohm's law to solve for the current in the circuit.

### Example Question #11 : Ap Physics 2

A student assembles a circuit made up of a voltage source and two resistors. All three circuit elements are connected in series. If the voltage across the voltage source is  and the resistance of the resistors are and  respectively, what is current through the second resistor?

Explanation:

Recall that the current through resistors connected in series is the equal for all components. The current through the first resistor and the current through the second resistor should be the same.

The first step in solving involves calculating the equivalent resistance of the circuit. Since the resistors are in series the equivalent resistance of this circuit is the sum of the two resistances.

Now we can use Ohm’s law to solve for the current.

### Example Question #1 : Electric Circuits

A charge travels along a copper wire that has a resistance of . It takes two seconds for the charge to travel along the wire. The potential difference in the wire is . What is the charge of the particle?

Explanation:

To solve this question you need to use the Ohm’s law and the definition of an electric current. Ohm’s law states that voltage is the product of current and resistance:

The definition of electric current is given by the charge per unit time:

Using these equations it is possible to solve for the charge. The trick is to first solve for the current using Ohm’s law and the given voltage and resistance.

Now that we know the current and the time, we can solve for the charge using our second equation.

### Example Question #1 : Electric Circuits

Which of the following is not equivalent to a unit of power?

Explanation:

The standard unit for power is Watts, but other equivalent units can be derived from the equations for power.

Remember that power is defined as work per unit time:

The units from this equation will be Joules per second, eliminating that answer choice.

In terms of circuits, power is defined as the product of current and voltage, giving the units Ampere-Volts:

If you combine Ohm’s law and the definition of power you can rewrite the equation for power as follows:

These units will be Amperes squared times Ohms.

The only answer choice you are left with is Ohm-Volts. Power in terms of resistance and voltage is:

### Example Question #11 : Ap Physics 2

Consider two resistors connected in series. Which of the following is true regarding its voltage, current, and power?

The voltage across both resistors is the same, but the larger resistor will have higher current and power dissipation

The voltage across both resistors is the same, but the smaller resistor will have higher current and power dissipation

The current through both resistors is the same, but the smaller resistor will have higher voltage and power dissipation

The current through both resistors is the same, but the larger resistor will have higher voltage and power dissipation

The current through both resistors is the same, but the larger resistor will have higher voltage and power dissipation

Explanation:

Since the resistors are connected in series, they will have the same current flowing through them. In series current is constant across resistors, and in parallel voltage is constant across resistors.

Remember the equations for voltage and power. The equation for voltage is Ohm's law:

Power can be written in terms of voltage and resistance, but in this problem only the current is held constant (because the resistors are in series) while the voltage of the resistors is different. The appropriate equation to use for comparison is:

From the equations you can deduce that increasing resistance will increase both voltage and power. The best answer is that current through both resistors is the same, but the larger resistor will have higher voltage and power dissipation.

### Example Question #1 : Electric Circuits

Which of the following changes to a copper wire will lead to the greatest decrease in voltage?

Replacing the copper wire with a more conductive material

Increasing the cross-sectional area of the copper wire by a factor of two

Increasing the length of the copper wire by a factor of two

Increasing the current through the copper wire by a factor of two

Increasing the cross-sectional area of the copper wire by a factor of two

Explanation:

According to Ohm’s law a decrease in current and/or resistance will lead to a decrease in voltage, since voltage is directly proportional to both current and resistance.

Increasing the current will not decrease voltage. Remember that resistance is defined as:

In this formula, is the resistivity, is the length of the wire, and  is the cross-sectional area of the wire. Increasing length will lead to an increase in resistance and voltage; however, increasing the area will lead to a decrease in resistance and, subsequently, a decrease in voltage.

The only answer that will lead to a decrease in voltage is the choice to increase the cross-sectional area of the wire.

Replacing the copper wire with a more conductive material will increase the resistivity, which will subsequently increase resistance and voltage.

### Example Question #1 : Understanding Resistors And Resistance

A student assembles a circuit made up of a voltage source and two resistors. All three circuit elements are connected in parallel. The voltage across the voltage source is  and the resistance of the resistors are and  respectively. Which of the following is true of this circuit?

The current through the  resistor will be less than the current through the resistor

The voltage across the  resistor will equal the voltage across the resistor

The current through the  resistor will equal the current through the resistor

The voltage across the  resistor will be less than the voltage across the resistor