# Test Prep for AP® Courses

### 3.1 Current

Which of the following can be explained on the basis of conservation of charge in a closed circuit consisting of a battery, resistor, and metal wires?

- The number of electrons leaving the battery will be equal to the number of electrons entering the battery.
- The number of electrons leaving the battery will be less than the number of electrons entering the battery.
- The number of protons leaving the battery will be equal to the number of protons entering the battery.
- The number of protons leaving the battery will be less than the number of protons entering the battery.

When a battery is connected to a bulb, there is 2.5 A of current in the circuit. What amount of charge will flow though the circuit in a time of 0.5 s?

- 0.5 C
- 1 C
- 1.25 C
- 1.5 C

If 0.625 × 10^{20} electrons flow through a circuit each second, what is the current in the circuit?

Two students calculate the charge flowing through a circuit. The first student concludes that 300 C of charge flows in 1 minute. The second student concludes that 3.125 × 10^{19} electrons flow per second. If the current measured in the circuit is 5 A, which of the two students (if any) have performed the calculations correctly?

### 3.2 Ohm’s Law: Resistance and Simple Circuits

If the voltage across a fixed resistance is doubled, what happens to the current?

- It doubles.
- It halves.
- It stays the same.
- The current cannot be determined.

The table below gives the voltages and currents recorded across a resistor.

Voltage (V) | 2.50 | 5.00 | 7.50 | 10.00 | 12.50 |

Current (A) | 0.69 | 1.38 | 2.09 | 2.76 | 3.49 |

- Plot the graph and comment on the shape.
- Calculate the value of the resistor.

What is the resistance of a bulb if the current in it is 1.25 A when a 4 V voltage supply is connected to it? If the voltage supply is increased to 7 V, what will be the current in the bulb?

### 3.3 Resistance and Resistivity

Which of the following affect the resistivity of a wire?

- Length
- Area of cross section
- Material
- All of the above

The lengths and diameters of four wires are given as shown.

If the four wires are made from the same material, which of the following is true? Select *two* answers.

- Resistance of Wire 3 > Resistance of Wire 2
- Resistance of Wire 1 > Resistance of Wire 2
- Resistance of Wire 1
- Resistance of Wire 4

Suppose the resistance of a wire is *R* Ω. What will be the resistance of another wire of the same material having the same length but double the diameter?

*R*/2- 2
*R* *R*/4- 4
*R*

The resistances of two wires having the same lengths and cross section areas are 3 Ω and 11 Ω. If the resistivity of the 3 Ω wire is 2.65 × 10^{−8} Ω∙m, find the resistivity of the 1 Ω wire.

The lengths and diameters of three wires are given below. If they all have the same resistance, find the ratio of their resistivities.

Wire |
Length |
Diameter |

Wire 1 | 2 m | 1 cm |

Wire 2 | 1 m | 0.5 cm |

Wire 3 | 1 m | 1 cm |

Suppose the resistance of a wire is 2 Ω. If the wire is stretched to three times its length, what will be its resistance? Assume that the volume does not change.

### 3.4 Electric Power and Energy

The circuit shown contains a resistor *R* connected to a voltage supply. The graph shows the total energy *E* dissipated by the resistance as a function of time. Which of the following shows the corresponding graph for double resistance, i.e., if *R* is replaced by 2*R*?

What will be the ratio of the resistance of a 120 W, 220 V lamp to that of a 100 W, 110 V lamp?