Current & Circuits

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课程笔记

Circuit Diagrams

  • Circuit symbols are used to represent electrical components in circuit diagrams and are universally recognised by scientists in any language.
  • A cell converts chemical energy to electrical energy; the direction of conventional current flow is from the positive (longer side) to the negative (shorter side) terminal.
  • A battery is a power source made up of multiple cells.
  • A switch turns the circuit on (closed) or off (open), allowing or preventing the flow of current.
  • A voltmeter measures potential difference and is connected in parallel; an ammeter measures current and is connected in series.
  • A fixed resistor increases resistance to limit current; a variable resistor has a slider to change its resistance.
  • An LDR (light-dependent resistor) has resistance that decreases as light intensity increases; a thermistor has resistance that decreases as temperature increases.
  • A diode (including an LED) allows current to flow in one direction only.

Electrical symbols used in circuit diagrams

Electrical symbols used in circuit diagrams

Electric Current

  • Electric current is the rate of flow of charge carriers, measured in amperes (A).
  • Charge is measured in coulombs (C); the greater the flow of charge, the greater the current.
  • The equation for current is I = Δq / Δt, where I is current (A), Δq is charge (C), and Δt is time (s).
  • Conventional current is defined as the flow of positive charge from the positive terminal to the negative terminal of a cell.
  • In metal wires, current is a flow of electrons, which are negatively charged and flow from the negative terminal to the positive terminal — opposite to conventional current.
  • Direct current (dc) flows in one direction only and is produced by cells and batteries.
  • Current is measured using an ammeter connected in series; an ideal ammeter has zero resistance.

Potential difference in a circuit

Potential difference in a circuit

Electric Potential Difference

  • Potential difference (p.d.), also called voltage, is the work done per unit charge on moving a positive charge between two points along the path of the current.
  • Potential difference is measured in volts (V) and calculated as V = W / q, where W is work done (J) and q is charge (C).
  • One volt is equal to one joule per coulomb: 1 V = 1 J C⁻¹.
  • In a d.c. circuit, the potential difference is provided by cells or batteries; each cell has a positive terminal (high potential) and a negative terminal (low potential).
  • A battery is a collection of cells arranged positive terminal to negative terminal.
  • The electronvolt (eV) is the amount of energy needed to move an electron through a potential difference of one volt; 1 eV = 1.6 × 10⁻¹⁹ J.

Electrical Conductors & Insulators

  • A conductor is a material that allows charge (usually electrons) to flow through it easily; examples include silver, copper, aluminium, and steel.
  • Conductors tend to be metals and are made up of positively charged metal ions within a sea of delocalised electrons.
  • Metals are excellent conductors because they contain a large number of delocalised electrons that are able to flow easily.
  • An insulator is a material with very few free charges, so it does not allow the flow of charge easily; examples include rubber, plastic, glass, and wood.
  • Insulators can conduct static electricity when charge builds up on their surface; when a charged insulator contacts a conductor, the charge can be transferred.

Conductors and insulators

Conductors and insulators

Electric Resistance

  • As electrons move through a conductor, they collide with metal ions and transfer some of their electrical potential energy to the positive ions, raising the internal energy of the metal and causing heating.
  • Resistance is defined as the ratio of the potential difference across a component to the current flowing through it: R = V / I.
  • The unit of resistance is the ohm (Ω); 1 Ω = 1 kg m² s⁻³ A⁻².
  • The higher the resistance of a component, the lower the current flowing through it, and vice versa.
  • An ideal voltmeter has infinite resistance so no current passes through it; an ideal ammeter has zero resistance so all the current passes through it.
  • Copper has a low electrical resistance, making it an ideal material for making wires.

Resistance in a conductor

Resistance in a conductor

Electrical Resistivity

  • The resistance of a sample depends on the material it is made of, its length, and its cross-sectional area.
  • The resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area.
  • Resistivity is the property describing the extent to which a material opposes the flow of electric current through it.
  • Resistivity is defined as the resistance per unit length of a material with unit cross-sectional area: ρ = RA / L.
  • Resistivity is measured in ohm-metres (Ω m) and is a property of the material.
  • Conductors such as metals have low values of resistivity, making them ideal for wires; insulators have very high resistivity, so virtually no current flows through them.
  • The cross-sectional area of a wire is modelled as a circle: A = πr² or A = πd²/4.

I-V Characteristics

  • Ohm's law states that for a component at constant temperature, the current through it is proportional to the potential difference across it: V = IR.
  • An electrical component obeys Ohm's law if its graph of current against potential difference is a straight line through the origin.
  • A fixed resistor is an ohmic component; a filament lamp is a non-ohmic component.
  • For an ohmic component, resistance can be determined from the gradient of an I-V graph: if I is on the y-axis and V on the x-axis, R = 1/gradient; if V is on the y-axis and I on the x-axis, R = gradient.
  • A semiconductor diode is forward-biased when current flows in the direction of the arrowhead symbol, showing a sharp increase in current; it is reverse-biased when it does not conduct and current is zero.
  • A filament lamp behaves approximately as an ohmic component at low voltages, but as voltage increases, the filament temperature and resistance increase, making it non-ohmic with a curve of decreasing gradient.
  • Non-ohmic devices include lamps, LEDs, thermistors, and LDRs.

Series & Parallel Circuits

  • In a series circuit, the current is the same at any point and the potential difference is split across all components depending on their resistance.
  • The combined resistance of resistors in series is the sum of the individual resistances: R = R₁ + R₂ + R₃.
  • Connecting more resistors in series increases the overall resistance; the combined resistance is more than the resistance of any individual component.
  • In a parallel circuit, the total current is equal to the sum of the currents in each parallel branch, and the potential difference is the same across each loop.
  • The reciprocal of the combined resistance of resistors in parallel is the sum of the reciprocals of the individual resistances: 1/R = 1/R₁ + 1/R₂.
  • Connecting more resistors in parallel decreases the overall resistance; the combined resistance is less than the resistance of any individual component.

A simple series circuit

A simple series circuit

Electrical Power

  • When an electrical current does work against electrical resistance, electrical energy is dissipated as thermal energy in the surroundings.
  • The amount of heat produced depends on the current (greater current produces more heat) and the resistance (higher resistance produces more heat for a given current).
  • Electrical power is the rate of change of work done: P = E / t = W / t, where P is power (W), E is energy transferred (J), and t is time (s).
  • Power dissipated by an electrical device can be written as P = IV, where I is current (A) and V is potential difference (V).
  • Using Ohm's law, power can also be written as P = I²R = V²/R.
  • The energy transferred can be written as E = VIt.
  • For a given resistor, doubling the current (or voltage) yields an electrical power four times greater.

Sources of Electrical Energy

  • An electric cell stores chemical energy that can be transferred to electrical energy.
  • Chemical cells (batteries) utilise chemical reactions to provide a potential difference; they can be rechargeable or non-rechargeable.
  • Non-rechargeable batteries (e.g. alkaline AA) can only be used once; rechargeable cells (e.g. lithium-ion, lead-acid) can be used many times as the chemical reaction is reversed when charged.
  • Solar cells (photovoltaic cells) convert electromagnetic radiation (photons) from the Sun into electrical energy.
  • Advantages of single-use batteries include high energy density, portability, and low cost; disadvantages include limited power supply, high internal resistance, and disposal issues.
  • Advantages of rechargeable batteries include high energy density, high electrical efficiency, and low internal resistance; disadvantages include degradation over time and higher cost.
  • Solar cells have an unlimited supply of clean energy but variable output dependent on weather and require large investment and areas.

Electromotive Force & Internal Resistance

  • Electromotive force (e.m.f.) is the amount of chemical energy converted to electrical energy per coulomb of charge when a charge passes through a power supply.
  • E.m.f. is measured in volts (V) and is also the potential difference across the cell when no current is flowing (open circuit).
  • E.m.f. is measured by connecting a high-resistance voltmeter across the terminals of the cell in an open circuit.
  • All power supplies have some internal resistance (r) between their terminals, which causes charge circulating to dissipate some electrical energy from the power supply itself, making the cell warm.
  • A cell can be considered as a source of e.m.f. with an internal resistance connected in series; the e.m.f. is the sum of the potential differences: ε = I(R + r).
  • The potential difference across the internal resistance is called the 'lost volts' (Vr = Ir); the terminal p.d. is the p.d. across the load resistor (VR = IR).
  • E.m.f. is the total, or maximum, voltage available to the circuit.

Variable Resistance

  • A thermistor is a non-ohmic, sensory resistor whose resistance varies with temperature; most are negative temperature coefficient (ntc), meaning resistance decreases as temperature increases.
  • Thermistors are used as temperature sensors in circuits such as ovens, fire alarms, and digital thermometers.
  • A light-dependent resistor (LDR) is a non-ohmic, sensory resistor whose resistance decreases as light intensity increases.
  • In the dark, an LDR's resistance is very large (millions of ohms); in bright light, its resistance is small (tens of ohms).
  • LDRs are used in automatic street lights and garden lights that switch on when it gets dark.
  • A potentiometer is similar to a variable resistor connected as a potential divider to give a continuously variable output voltage; it can be used to compare potential differences in different parts of a circuit.
  • Moving the slider on a potentiometer changes the resistance (and hence potential difference) of the upper and lower parts, allowing maximum or minimum output voltage.

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练习题

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  1. 1.What is the unit of electric current?

    Easy
    • AVolt
    • BAmpere
    • CCoulomb
    • DOhm

  2. 2.Which of the following is the correct definition of the coulomb?

    Easy
    • AThe charge transferred by a current of 1 A in 1 s
    • BThe charge on one electron
    • CThe energy transferred by a potential difference of 1 V
    • DThe resistance when 1 V drives 1 A

  3. 3.A charge of 60 μC flows through a conductor in 140 ms. What is the current in the conductor?

    Easy
    • A0.43 mA
    • B0.43 A
    • C4.3 mA
    • D430 mA

  4. 4.Which of the following statements about conventional current and electron flow is correct?

    Medium
    • AConventional current flows from negative to positive; electrons flow from positive to negative.
    • BConventional current flows from positive to negative; electrons flow from negative to positive.
    • CBoth conventional current and electron flow are from positive to negative.
    • DBoth conventional current and electron flow are from negative to positive.

  5. 5.A student builds a circuit with a 6.0 V battery and two resistors of 4.0 Ω and 8.0 Ω connected in parallel. What is the total current drawn from the battery?

    Medium
    • A0.50 A
    • B2.25 A
    • C1.50 A
    • D0.75 A

  6. 6.A wire of length L and cross-sectional area A has resistance R. If the wire is stretched to twice its original length while its volume remains constant, what is its new resistance?

    Medium
    • A2R
    • B4R
    • CR/2
    • DR/4

  7. 7.Which of the following best explains why an ideal ammeter should have zero resistance?

    Medium
    • ASo that it does not change the current it is measuring
    • BSo that it can measure very large currents
    • CSo that it does not affect the potential difference across the component
    • DSo that it can be connected in parallel with the component

  8. 8.Which of the following is an ohmic conductor?

    Medium
    • AFilament lamp
    • BLight-emitting diode
    • CFixed resistor at constant temperature
    • DThermistor

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