Electricity · Lesson 2 of 9
Electric Potential and Potential Difference
“Potential difference gives charges the push they need to stop being couch potatoes.”
• Explain why a source is needed to maintain charge flow in a circuit. • Interpret potential difference as work done per unit charge. • Use the relationship among work, charge and potential difference. • State the meaning of one volt and use joule-per-coulomb units. • Connect a voltmeter correctly across two points.
Water does not continue flowing between two containers at the same level; a difference in level or pressure is needed. In a similar way, charges require an electrical difference between two points before they move steadily through a component. A cell creates and maintains this difference by converting chemical energy into electrical energy.
The work done to move a unit charge from one point to another in an electric circuit.
A potential difference of 1 V means that 1 J of work is done when 1 C of charge moves between the two points. Thus 1 V = 1 J/C. The value describes energy transferred per coulomb, not the total energy. If twice as much charge moves across the same potential difference, twice as much energy is transferred.
Role of a Cell or Battery
Chemical reactions inside a cell separate charge and maintain different electric potentials at its terminals. When the circuit is closed, the source supplies energy to move charge through the circuit. A battery is a combination of cells and can maintain a larger or more useful potential difference depending on its arrangement.
Potential difference can exist even when no current flows, just as pressure can exist behind a closed valve. Current begins only when a complete conducting path is provided. The source supplies energy; the circuit components transform that energy into light, heat, motion or other forms.
Measuring Potential Difference
A voltmeter is connected in parallel across the two points being compared. It therefore has one terminal at each end of the component. Its positive terminal is connected toward the higher-potential side. A voltmeter is designed with high resistance so that it draws very little current and changes the circuit as little as possible.
| Quantity | Meaning | Instrument | Connection |
|---|---|---|---|
| Current | Charge passing per unit time | Ammeter | Series |
| Potential difference | Energy transferred per unit charge | Voltmeter | Parallel |
A Reliable Solving Method
- Write W in joules and Q in coulombs.
- Identify whether V, W or Q must be found.
- Use V = W/Q and rearrange symbolically.
- Interpret the result as energy per coulomb.
- Check that increasing charge at fixed voltage increases total work proportionally.
Problem
How much work is done when 2 C passes through a potential difference of 12 V?
- 1.Given: Q = 2 C and V = 12 V. Required: W.
- 2.From V = W/Q, rearrange to W = VQ.
- 3.W = 12 V × 2 C = 24 J.
- 4.The answer is reasonable: each coulomb receives 12 J, so two coulombs receive 24 J.
Problem
A source transfers 360 J while moving 30 C. Find the potential difference.
- 1.Given: W = 360 J and Q = 30 C. Required: V.
- 2.Use V = W/Q.
- 3.V = 360 J ÷ 30 C = 12 J/C = 12 V.
- 4.The source transfers 12 J of energy to each coulomb.
Problem
A 9 V battery transfers 5.4 kJ of energy. Find the charge moved and the time if the current is 0.50 A.
- 1.Given: V = 9 V, W = 5.4 kJ = 5400 J and I = 0.50 A.
- 2.First use Q = W/V = 5400/9 = 600 C.
- 3.Then use I = Q/t, so t = Q/I = 600/0.50 = 1200 s.
- 4.Convert: 1200 s = 20 min.
- 5.Check: 0.50 A for 1200 s transfers 600 C, and 9 J/C × 600 C = 5400 J.
Quiz
What does a potential difference of 6 V mean?
How is a voltmeter connected to measure voltage across a resistor?
A source does 80 J of work on 20 C. What is the potential difference?
Which statement is correct?
If charge doubles across the same potential difference, what happens to work done?
Practice Problems
- Find the work done in moving 5 C through 20 V. Solution: W = VQ = 20 × 5 = 100 J.
- A source does 450 J of work while moving 25 C. Find V. Solution: V = W/Q = 450/25 = 18 V.
- How much charge is moved when 240 J is transferred across 12 V? Solution: Q = W/V = 240/12 = 20 C.
- A 6 V battery moves 300 C. Find the energy transferred. If this occurs in 2 minutes, find the current. Solution: W = VQ = 6 × 300 = 1800 J. t = 120 s, so I = Q/t = 300/120 = 2.5 A.
- A student connects a voltmeter in series and an ammeter across a cell. Explain both errors. Solution: A voltmeter must be parallel because it compares two points and has high resistance. An ammeter must be series; across a cell its low resistance could produce a dangerously large current.
Key Takeaways
• Potential difference is energy transferred per unit charge. • One volt equals one joule per coulomb. • A cell maintains potential difference by converting chemical energy. • Potential difference can exist without current, but steady current requires a closed path. • A voltmeter is connected in parallel and an ammeter in series. • Work, charge and voltage are linked by W = VQ. • Current and potential difference describe different features of a circuit.