Potential difference, energy and power
Section: Electricity | Syllabus: Cambridge AS Level Physics 9702
Potential Difference Potential difference (p.d.) between two points is defined as the energy transferred per unit charge passing between those points. Potential Difference The energy transferred per unit charge: V = fraction where V = potential difference (V), W = energy transferred (J), Q = charge (C) Potential difference is measured in volts (V) .
One volt is the p.d. between two points when one joule of energy is transferred per coulomb of charge passing between them. Unit Relationship 1 V = 1 J C^-1 (one joule per coulomb) Rearranging the Equation The equation V = fraction can be rearranged to find: Energy transferred: W = VQ Charge: Q = fraction Since Q = It, we can also write: W = VIt Energy Transfer in Circuits FIG 9.6: Simple Circuit Showing Current and Potential Difference Show a cell connected in series with an ammeter (A) and a lamp.
A voltmeter (V) is connected in parallel across the lamp to measure the potential difference. As charge moves around a circuit, energy is transferred: In the power supply: Work is done ON the charges, increasing their electrical potential energy.
Chemical energy (battery) or other forms are converted to electrical energy. In circuit components: Work is done BY the charges, transferring electrical energy to other forms (thermal, light, kinetic, etc.).
Energy Conservation The total energy supplied by the source equals the total energy transferred in all components (conservation of energy). Worked Example: Energy and Charge Question: What is the potential difference across a motor when 30 C of charge passing through it transfers 90 J of energy?
Solution V = fraction = fraction = 3 V Worked Example: Calculating Charge Question: An electric motor runs from a 9 V battery and does 180 J of work. What charge passes through the motor? Solution Q = fraction = fraction = 20 C Electrical Power Power is the rate of energy transfer (or rate of doing work).
Power P = fraction where P = power (W), W = energy transferred (J), t = time (s) Power is measured in watts (W) . One watt equals one joule per second (1 W = 1 J s^-1). Electrical Power Equations For electrical circuits, power can be expressed in several equivalent forms: Equation Form Useful When You Know P = VI Primary form Voltage and current P = I^2R Derived using V = IR Current and resistance P = fraction Derived using I = fraction Voltage and resistance Derivation of Power Equations Deriving P = VI Starting from the definitions of potential difference and power: V = fraction so W = VQ P = fraction = fraction Since I = fraction, we have fraction = I Therefore: P = VI Deriving P = I²R Starting from P = VI and substituting V = IR: P = VI = (IR) × I = I^2R Deriving P = V²/R Starting from P = VI and substituting I = fraction: P = VI = V × fraction = fraction Exam Tip You must be able to derive these equations from P = VI and Ohm's law.
Examiners often ask for derivations. Interpreting Power Ratings Electrical appliances have power ratings that indicate the rate at which they transfer energy under normal operating conditions. For example, a "650 W" heater transfers 650 joules of electrical energy to thermal energy every second when operating at its rated voltage.
Worked Example: Power Calculation Question: A lamp rated at 3.0 V passes a current of 500 mA. What is its power output? Solution Convert current: I = 500 mA = 0.50 A P = VI = 3.0 × 0.50 = 1.5 W Worked Example: Finding Current from Power Question: An electric shower has a power output of 7.7 kW and operates at 230 V.
Calculate the current. Solution P = VI so I = fraction I = fraction = 33 A (to 2 s.f.) Energy Transferred by Electrical Devices The energy transferred by an electrical device can be calculated using: Energy Equations W = Pt = VIt = I^2Rt = fraction Worked Example: Energy Calculation Question: A 2.0 kW kettle is used for 3.0 minutes.
Calculate the energy transferred. Solution Convert time: t = 3.0 × 60 = 180 s W = Pt = 2000 × 180 = 360\,000 J = 360 kJ Worked Example: Combined Calculation Question: A 12 V power supply is connected to a lamp with resistance 6.0 Ω.
Calculate (a) the current, (b) the power, and (c) the energy transferred in 5.0 minutes. Solution (a) Current: I = fraction = fraction = 2.0 A (b) Power: P = VI = 12 × 2.0 = 24 W Or: P = fraction = fraction = 24 W (c) Energy transferred: W = Pt = 24 × (5.0 × 60) = 24 × 300 = 7200 J = 7.2 kJ The Kilowatt-Hour (kWh) For practical purposes, electrical energy is often measured in kilowatt-hours (kWh) rather than joules.
Kilowatt-Hour 1 kWh = energy transferred by a 1 kW device operating for 1 hour 1 kWh = 1000 W × 3600 s = 3.6 × 10^6 J = 3.6 MJ Worked Example: Energy in kWh Question: A 650 W microwave is used for 4 minutes.
Calculate the energy transferred in (a) joules and (b) kWh. Solution (a) In joules: W = Pt = 650 × (4 × 60) = 650 × 240 = 156\,000 J (b) In kWh: Power = 0.65 kW, Time = fraction hours = fraction hours Energy = 0.65 × fraction = 0.043 kWh Common Exam Mistakes Confusing V for volts an…
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