Question

A certain $9\mathrm{V}$ battery is used as a power source to move a $2\mathrm{C}$ charge. How much work is done by the battery? (A) $4.5\mathrm{J}$ (B) $9\mathrm{J}$ (C) $18\mathrm{J}$ (D) $36J$

Short answer

9 J

Step-by-step solution

- Understand the Formula

The work done by a battery is given by the formula:

- Identify the Given Values

From the problem, the voltage (V) of the battery is voltage on second note --which includes identifying charge, the as 9whhch in notations ie.g value of Voltage simple, converting ...

- Plug in the Values

Use the given values to substitute into the formula to calculate work. The voltage of the battery is 9V and the charge moved is 2C. Therefore: Work = ... will provide us with the required .

- Calculate the Work Done

Now, calculate the work done: Work = 9V multiplied by charge value which is equal simply 9 times by 2 it will result to final value of

- Select the Correct Answer

From multiple choice: identify the correct choice includes under choices B. Therefore corrects the input.

Key concepts

Voltage and Charge Relationship

Voltage and charge are directly related to the work done by a battery. When you move an electric charge through a potential difference (voltage), the battery performs work. The essential formula here is:

$W=V\times Q$

where $W$ is the work done, $V$ is the voltage, and $Q$ is the charge.

For example, if you have a battery with 9 volts (V) and it moves a charge of 2 coulombs (C), plugging these values into the formula gives you:

$$W=9V\times 2C=18J$$

This means the battery does 18 joules of work to move the charge. Understanding this relationship can help you predict how much work will be done with different voltages and charges. This direct proportionality makes it easier to calculate work in various scenarios involving electrical systems.

Work-Energy Principle

The work-energy principle states that the work done on an object results in a change in its energy. In the case of electrical systems, the work done by moving a charge through a voltage difference changes the electrical potential energy of the charge.

Think of the battery as a pump that lifts water to a higher level. The energy expended to lift the water increases its potential energy. Similarly, a battery 'lifts' electric charges through its potential difference (voltage), increasing their electrical potential energy.

The work done by the battery, calculated with $W=V\times Q$, is an energy transformation from the chemical energy in the battery to the electrical potential energy of the charge. The conversion of this energy underlines the work-energy principle and shows how energy is conserved and transformed in an electrical circuit.

Electric Potential Energy

Electric potential energy is the energy stored in an electric charge due to its position in an electric field. In a circuit, this energy is provided by a battery or power source.

When a battery moves a charge, it changes the electric potential energy. For instance, with our 9V battery moving a 2C charge, the charge gains potential energy:

$$U=V\times Q=9V\times 2C=18J$$

The potential energy gained by the charge is 18 joules. This stored energy can be converted into other forms, like kinetic or thermal energy, when the charge moves through the circuit.

Understanding electric potential energy is important in analyzing how circuits work, how energy is stored, and how it is transformed and utilized.