If 36 J of work is done in moving a charge Q across 8 V, find Q (in coulombs).
4.5
Calculating Charge from Work and Potential Difference
This problem requires us to find the amount of charge (Q) moved when a specific amount of work (W) is done against a given potential difference (V). The fundamental relationship connecting these three quantities is:
Work Done (\(W\)) = Charge (\(Q\)) \(\times\) Potential Difference (\(V\))
The units for these quantities in the SI system are Joules (J) for work, Coulombs (C) for charge, and Volts (V) for potential difference.
We are given:
- Work done, \(W = 36\) J
- Potential difference, \(V = 8\) V
We need to find the charge, \(Q\). We can rearrange the formula to solve for \(Q\):
\(Q = \frac{W}{V}\)
Now, substitute the given values into the rearranged formula:
\(Q = \frac{36 \text{ J}}{8 \text{ V}}\)
Performing the division:
\(Q = 4.5 \text{ C}\)
So, the charge moved across the 8 V potential difference, with 36 J of work done, is 4.5 Coulombs.
Let's look at the given options:
- Option 1: 288
- Option 2: 9
- Option 3: 4.5
- Option 4: 16
Our calculated value of 4.5 Coulombs matches Option 3.
Revision Table: Key Concepts
| Concept | Symbol | SI Unit | Formula Relation |
|---|---|---|---|
| Work Done | \(W\) | Joule (J) | \(W = Q \times V\) |
| Charge | \(Q\) | Coulomb (C) | \(Q = W / V\) |
| Potential Difference | \(V\) | Volt (V) | \(V = W / Q\) |
Additional Information: Understanding Work, Charge, and Voltage
Work (W): In the context of electricity, work is done when a force causes a charge to move over a distance against an electric field. It represents the energy transferred.
Charge (Q): Charge is a fundamental property of matter. It is measured in Coulombs (C). A Coulomb is a large unit; electron charge is about \(1.602 \times 10^{-19}\) C.
Potential Difference (V): Also known as voltage, it is the difference in electric potential energy per unit charge between two points in an electric circuit. It represents the energy required to move a unit charge between those points. One Volt is equal to one Joule per Coulomb (\(1 \text{ V} = 1 \text{ J/C}\)). This unit relationship directly explains why \(W/V\) gives the charge \(Q\) in Coulombs.
Understanding the relationship \(W = QV\) is crucial for solving problems involving energy transfer in electric fields or circuits. This problem is a direct application of this fundamental formula.
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