Question

A charge of 2 ?C flows from the positive terminal of a 6 V battery, through a 100 ? resistor, and back through the battery to the positive terminal. What is the total potential difference experienced by the charge? (A) 0 V (B) 0.002 V (C) 0.2 V (D) 6 V

Short answer

(D) 6 V

Step-by-step solution

Understand Potential Difference

The potential difference, or voltage, is the difference in electric potential between two points in a circuit.

Analyzing the Battery Voltage

The battery provides a potential difference (voltage) of 6 V. This means that 6 V is the amount of work done to move the charge around the circuit.

Consider the Resistor

While a resistor would drop some voltage when a current flows through it, the problem requires the total potential difference experienced by the charge over the entire circuit, including both the resistor and the battery.

Total Potential Difference Calculation

The total potential difference experienced by the charge is determined by the voltage provided by the battery, since the charge returns to the same point after completing the circuit. Therefore, the total potential difference remains the same as the voltage of the battery.

Conclusion

The total potential difference experienced by the charge flowing from the positive terminal of the battery, through the resistor, and back to the positive terminal is 6 V.

Key concepts

voltage in circuits

Voltage, often referred to as electric potential difference, is a key concept in understanding how electrical circuits work. It's the measure of how much energy is needed to move a charge from one point to another in a circuit. Picture it as the 'push' that makes electrons flow.
Without voltage, there is no current. When you connect a source like a battery to a circuit, it creates this voltage, enabling the circuit to function.
For example:

• A battery with a higher voltage can push more electrons through a circuit, creating a stronger current.
• Every component in the circuit, like resistors, uses up some of this voltage.

electric potential

Electric potential is a broader term that extends beyond just circuits. It deals with the potential energy a charge has due to its position in an electric field.
In circuits, electric potential helps explain how much work is needed to move a charge between two points. Remember, work in physics terms relates to energy transfer.
Here's how it connects to voltage:

• If you have a high electric potential difference between two points, a lot of work will be needed to move the charge.
• This work translates directly into the voltage in a circuit, making the concepts closely related.

So, whenever you hear electric potential, think about the energy and how it translates into volts in practical applications.

battery voltage

When we talk about a battery in a circuit, we're referring to a device that provides a constant voltage. This voltage is crucial as it determines the overall energy available to move charges through the circuit.
Key points to understand about battery voltage:

• The value of battery voltage tells you how much work it can do. For instance, a 6 V battery can move charges with more energy than a 1.5 V battery.
• In a complete circuit, charges flow from the positive terminal, through the circuit, and return to the negative terminal.

Batteries maintain a fixed voltage despite changes in the circuit. This stability is why they're so reliable in powering devices.
As seen in our exercise, a 6 V battery provides a potential difference that remains unchanged throughout the circuit.

resistor voltage drop

Resistors are components in a circuit that impede the flow of current, causing a drop in voltage across them. This drop can be explained by Ohm's law, which states that the voltage drop across a resistor is equal to the current times the resistance (V = IR).
In our exercise, here's how this works:

• When the charge flows through the 100 Ω resistor, it encounters resistance, causing a voltage drop.
• This voltage drop uses part of the battery's provided voltage. However, for the total circuit, the potential difference is still considered from start to end.

Even though there's a drop at each resistor, when considering the entire journey of the charge from the battery's positive terminal and back, the total voltage accounts for all these drops combined, affirming the total potential difference is the battery's voltage.