If 90 J of work is done in moving a charge of 2,000 coulombs across V volts, find V.
0.045
Solving for Voltage using Work and Charge
The question asks us to find the voltage (V) when a certain amount of work is done to move a specific amount of charge. This problem involves the relationship between work, charge, and potential difference (voltage) in an electrical circuit.
The fundamental formula connecting these quantities is:
$$ \text{Work Done (W)} = \text{Charge (Q)} \times \text{Voltage (V)} $$
This formula can be rearranged to solve for Voltage:
$$ \text{Voltage (V)} = \frac{\text{Work Done (W)}}{\text{Charge (Q)}} $$
In this specific problem, we are given the following values:
- Work Done (W) = 90 Joules (J)
- Charge (Q) = 2,000 Coulombs (C)
Now, we can substitute these values into the rearranged formula to find the voltage:
$$ V = \frac{W}{Q} $$
$$ V = \frac{90 \text{ J}}{2000 \text{ C}} $$
$$ V = \frac{90}{2000} \text{ Volts} $$
To simplify the fraction, we can divide both the numerator and the denominator by 10:
$$ V = \frac{9}{200} \text{ Volts} $$
Now, perform the division:
$$ V = 0.045 \text{ Volts} $$
Therefore, the voltage across which the charge is moved is 0.045 volts.
Calculation Summary: Work, Charge, and Voltage
| Quantity | Symbol | Value | Unit |
|---|---|---|---|
| Work Done | W | 90 | Joules (J) |
| Charge | Q | 2000 | Coulombs (C) |
| Voltage (to find) | V | ? | Volts (V) |
Formula used: $$ V = \frac{W}{Q} $$
Calculation: $$ V = \frac{90}{2000} = 0.045 \text{ V} $$
Revision Table: Key Concepts
| Term | Definition | Unit | Formula Relationship |
|---|---|---|---|
| Work | Energy transferred when a force moves an object over a distance; in electrical terms, energy transferred to move charge. | Joule (J) | $W = QV$ |
| Charge | A fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. | Coulomb (C) | $Q = W/V$ |
| Voltage (Potential Difference) | The difference in electrical potential energy per unit charge between two points in a circuit. It is the energy required per unit charge to move charge between the points. | Volt (V) | $V = W/Q$ |
Additional Information: Understanding Electrical Work and Voltage
Work done in moving a charge is the energy transferred to move that charge against an electric field. Voltage, or potential difference, represents how much energy is needed per unit of charge to move it from one point to another. A higher voltage means more energy is available to push each unit of charge through a circuit.
The relationship $W = QV$ is a core concept in electricity. It tells us that the total work done is proportional to both the amount of charge moved and the potential difference it moved across. If you double the charge or double the voltage, you double the work done.
Units are very important here:
- Work is measured in Joules (J).
- Charge is measured in Coulombs (C).
- Voltage is measured in Volts (V).
The formula $V = W/Q$ shows that 1 Volt is equivalent to 1 Joule per Coulomb ($1 \text{ V} = 1 \text{ J/C}$). This unit relationship is consistent with our calculation.
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