Current & Circuits

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Apuntes de la lección

Circuit Diagrams & Symbols

Circuit symbols are universally recognised and used to represent components in circuit diagrams.
A cell converts chemical energy to electrical energy; the longer line is the positive terminal, and conventional current flows from positive to negative.
A battery is a power source made of multiple cells connected positive to negative.
A switch turns the circuit on (closed) or off (open), allowing or preventing current flow.
A voltmeter measures potential difference and is connected in parallel; an ammeter measures current and is connected in series.
A fixed resistor limits current; a variable resistor has a slider to change resistance, which changes the current.
An LDR's resistance decreases as light intensity increases; a thermistor's resistance decreases as temperature increases.
A diode (including LED) allows current in one direction only; a potentiometer acts as an adjustable voltage divider.

Electrical symbols used in circuit diagrams

Electric Current

Electric current is the rate of flow of charge carriers, measured in amperes (A).
The equation for current is I = Δq / Δt, where Δq is charge in coulombs and Δt is time in seconds.
Conventional current flows from the positive terminal to the negative terminal of a cell.
In metals, electrons are the charge carriers and flow from negative to positive, opposite to conventional current.
Direct current (dc) flows in one direction only and is produced by cells and batteries.
Current is a scalar quantity; its sign indicates direction.

Potential difference in a circuit

Electric Potential Difference

Potential difference (p.d.) is the work done per unit charge on moving a positive charge between two points along the path of the current.
It is calculated as V = W / q, where W is work done in joules and q is charge in coulombs.
One volt is equal to one joule per coulomb (1 V = 1 J C⁻¹).
Potential difference is provided by cells or batteries; electrons gain electrical potential energy as they move through the cell.
The electronvolt (eV) is the 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 allows charge (usually electrons) to flow easily; examples include silver, copper, aluminium, and steel.
Metals are good conductors because they contain a large number of delocalised electrons that can flow freely.
An insulator has very few free charges and does not allow charge to flow easily; examples include rubber, plastic, glass, and wood.
Insulators can conduct static electricity when charge builds up on their surface and is transferred on contact with a conductor.

Conductors and insulators

Electric Resistance

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.
As electrons move through a conductor, they collide with metal ions, transferring energy and causing heating, which results in resistance.
The higher the resistance of a component, the lower the current flowing through it for a given potential difference.
An ideal ammeter has zero resistance so it does not affect the current it measures.
An ideal voltmeter has infinite resistance so no current passes through it.

Resistance in a conductor

Electrical Resistivity

The resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area.
Resistivity (ρ) 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 have low resistivity, making them ideal for wires; insulators have very high resistivity.
The cross-sectional area of a wire is modelled as a circle: A = πr² = πd²/4.
If the diameter of a wire doubles, its cross-sectional area quadruples, so its resistance drops to a quarter.

I-V Characteristics

Ohm's law states that for a component at constant temperature, current is proportional to potential difference: V = IR.
An ohmic component has an I-V graph that is a straight line through the origin; examples include fixed resistors and wires at constant temperature.
Non-ohmic components include filament lamps, diodes (LEDs), thermistors, and LDRs.
For a fixed resistor, resistance can be found from the gradient of an I-V graph: if I is on the y-axis, R = 1/gradient; if V is on the y-axis, R = gradient.
A filament lamp is approximately ohmic at low voltages, but as voltage increases, its temperature and resistance increase, making it non-ohmic.
A semiconductor diode conducts when forward-biased (current in direction of arrowhead) and has zero current when reverse-biased.

Series & Parallel Circuits

In a series circuit, the current is the same at any point, and the potential difference is split across components depending on their resistance.
The total resistance of resistors in series is the sum of individual resistances: R_total = R₁ + R₂ + R₃ + ...
In a parallel circuit, the total current is the sum of the currents in each 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 individual resistances: 1/R_total = 1/R₁ + 1/R₂ + ...
Adding resistors in series increases the total resistance; adding resistors in parallel decreases the total resistance.

A simple series circuit

Electrical Power

Electrical power is the rate of energy transfer: P = E / t = W / t.
Power can also be calculated as P = IV, where I is current and V is potential difference.
Using Ohm's law, power can be written as P = I²R = V²/R.
Doubling the current or voltage across a resistor increases the power by a factor of four.
The energy transferred is given by E = VIt.
The heat produced in a component depends on current and resistance; greater current or higher resistance produces more heat.

Power and rate of energy transfer

Sources of Electrical Energy

Electric cells store chemical energy and convert it to electrical energy; examples include chemical cells, solar cells, mains electricity, and wind generators.
Non-rechargeable batteries (e.g., alkaline AA) can only be used once; rechargeable cells (e.g., lithium-ion, lead-acid) can be recharged by reversing the chemical reaction.
Solar cells (photovoltaic cells) convert electromagnetic radiation from the Sun into electrical energy.
Advantages of rechargeable cells include high energy density, long lifetime, and low internal resistance; disadvantages include degradation over time and higher cost.
Solar cells have an unlimited supply of energy and are clean, but their output is variable and depends on weather conditions.
Wind generators have zero fuel costs and no chemical pollution, but have high set-up costs and inconsistent output.
Mains electricity from fossil fuels is reliable and has high energy density, but produces greenhouse gases and is non-renewable.

Electromotive Force & Internal Resistance

Electromotive force (e.m.f.) is the amount of chemical energy converted to electrical energy per coulomb of charge passing through a power supply.
E.m.f. is measured in volts (V) and is the potential difference across a cell when no current flows (open circuit).
Internal resistance (r) is the resistance within a power supply that causes a loss of voltage and heating of the cell.
A cell can be modelled as a source of e.m.f. in series with an internal resistance.
The e.m.f. equation is ε = I(R + r), where R is the external load resistance and r is the internal resistance.
The terminal potential difference is the p.d. across the load resistor and is less than the e.m.f. when current flows; the difference is the 'lost volts' (Ir).

Variable Resistance

A thermistor is a non-ohmic, temperature-dependent resistor; most are negative temperature coefficient (ntc), meaning resistance decreases as temperature increases.
Thermistors are used as temperature sensors in ovens, fire alarms, and digital thermometers.
A light-dependent resistor (LDR) is a non-ohmic resistor whose resistance decreases as light intensity increases.
LDRs are used in automatic lighting systems; in the dark, resistance is very high (millions of ohms), and in bright light, it is low (tens of ohms).
A potentiometer is a variable resistor connected as a potential divider to provide a continuously variable output voltage.
Moving the slider on a potentiometer changes the resistance and hence the potential difference across the upper and lower parts.

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Preguntas de práctica

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1.Which quantity is defined as the rate of flow of charge carriers?
Easy
- APotential difference
- BResistance
- CElectric current
- DElectrical power
2.Which statement correctly describes the direction of conventional current and electron flow in a metal wire?
Easy
- AConventional current flows from positive to negative; electrons flow from negative to positive
- BConventional current flows from negative to positive; electrons flow from positive to negative
- CBoth conventional current and electrons flow from positive to negative
- DBoth conventional current and electrons flow from negative to positive
3.An ideal ammeter should have zero resistance.
Easy
True or false?
4.A charge of 60 μC flows through a conductor in 140 ms. What is the current in the conductor?
Easy
- A0.43 mA
- B0.23 mA
- C4.3 mA
- D0.86 mA
5.Which of the following is the correct definition of potential difference?
Easy
- AThe rate of flow of charge carriers
- BThe work done per unit charge on moving a positive charge between two points
- CThe ratio of current to potential difference
- DThe amount of chemical energy converted to electrical energy per coulomb of charge
6.Two resistors of resistance 3.0 Ω and 6.0 Ω are connected in parallel. What is their combined resistance?
Medium
- A2.0 Ω
- B4.5 Ω
- C9.0 Ω
- D0.5 Ω
7.Which of the following statements about series and parallel circuits are correct? (select all that apply)
Medium
- AIn a series circuit, the current is the same at any point.
- BIn a parallel circuit, the potential difference is the same across each branch.
- CThe combined resistance of resistors in series is less than the smallest individual resistance.
- DThe combined resistance of resistors in parallel is greater than the largest individual resistance.
- EIn a series circuit, the potential difference is split across all components.
8.Match each electrical component with its correct function.
Medium
- Ammeter
- Voltmeter
- LDR
- Thermistor
- Measures current in a circuit
- Measures potential difference across a component
- Resistance decreases as light intensity increases
- Resistance decreases as temperature increases

Más preguntas

9.A wire made of copper has a resistance of 2.0 Ω. A second wire of the same material and length has twice the diameter. What is the resistance of the second wire?
Medium
- A0.5 Ω
- B1.0 Ω
- C4.0 Ω
- D8.0 Ω
10.Which of the following is an ohmic conductor?
Easy
- AFilament lamp
- BSemiconductor diode
- CFixed resistor at constant temperature
- DThermistor
11.The current-voltage graph for a filament lamp is a straight line through the origin.
Easy
True or false?
12.A battery has an emf of 9.0 V and internal resistance of 0.50 Ω. It is connected to a resistor of resistance 4.0 Ω. What is the terminal potential difference across the battery?
Medium
- A8.0 V
- B9.0 V
- C1.0 V
- D4.5 V
13.Which of the following is a secondary (rechargeable) cell?
Medium
- AAlkaline AA battery
- BLithium-ion battery
- CSolar cell
- DMains electricity
14.Which material is the best conductor of electricity?
Medium
- ARubber
- BGlass
- CCopper
- DWood
15.A diode only allows current to flow in one direction.
Easy
True or false?
16.A thermistor is connected in series with a fixed resistor R and a battery. At room temperature, the resistance of the thermistor equals the resistance of R. When the temperature of the thermistor decreases, which statement is correct?
Hard
- AThe potential difference across the thermistor increases
- BThe current in R increases
- CThe current through the thermistor decreases
- DThe potential difference across R increases
17.Which graph represents the variation of current I with potential difference V for a light-dependent resistor (LDR) in constant light intensity?
Medium
- AA curve with increasing gradient
- BA straight line through the origin
- CA curve with decreasing gradient
- DA horizontal straight line
18.Match each component with the correct circuit function.
Easy
- Ammeter
- Voltmeter
- Variable resistor
- Thermistor
- Measures current, connected in series
- Measures potential difference, connected in parallel
- Resistance can be changed using a slider
- Resistance decreases as temperature increases
19.Place the steps for calculating the resistance of a wire in the correct order.
Medium
- Measure the potential difference across the wire and the current through it
- Calculate the resistance using R = V / I
- Measure the length of the wire
- Calculate the cross-sectional area from the diameter
- Calculate the resistivity using ρ = RA / L
20.Which of the following statements about electrical power are correct? (select all that apply)
Medium
- APower dissipated by a resistor is given by P = I²R
- BPower dissipated by a resistor is given by P = V²/R
- CDoubling the current through a resistor doubles the power dissipated
- DPower is the rate of energy transfer
- EPower dissipated by a resistor is given by P = IR
21.Which of the following are true for a thermistor with a negative temperature coefficient? (select all that apply)
Hard
- AIts resistance decreases as temperature increases
- BIt is a non-ohmic component
- CIts I-V graph is a straight line through the origin
- DIt can be used as a temperature sensor
- EIts resistance increases as temperature increases
22.The resistivity of a material is equal to the resistance per unit length of a material with unit cross-sectional area.
Easy
True or false?
23.In a parallel circuit, the potential difference across each branch is the same.
Easy
True or false?
24.The internal resistance of a cell causes the terminal potential difference to be greater than the emf when current flows.
Medium
True or false?
25.Two resistors of resistance 3.0 Ω and 6.0 Ω are connected in series with a 12 V cell of negligible internal resistance and an ammeter. What is the reading on the ammeter?
Medium
- A1.3 A
- B2.0 A
- C4.0 A
- D6.0 A
26.Two resistors of resistance 3.0 Ω and 6.0 Ω are connected in parallel with a 12 V cell of negligible internal resistance and an ammeter. What is the reading on the ammeter?
Medium
- A1.3 A
- B2.0 A
- C4.0 A
- D6.0 A
27.The graph of current I against potential difference V for a filament lamp is a curve whose gradient decreases as V increases. What does this show about the resistance of the filament?
Medium
- AThe resistance decreases as V increases
- BThe resistance increases as V increases
- CThe resistance stays constant
- DThe resistance first increases then decreases
28.A student plots a graph of resistance R against length L for a wire of constant cross-sectional area. Which statements about using this graph to find the resistivity are correct? (select all that apply)
Hard
- AThe gradient of the graph is equal to ρ/A
- BThe resistivity is found by multiplying the gradient by A
- CThe graph should be a straight line through the origin
- DThe resistivity is found by dividing the gradient by A
- EThe graph should curve upwards
29.A resistor of resistance 2.5 kΩ and a cell with internal resistance are placed in a circuit. A current of 0.6 mA flows. What is the terminal potential difference reading on the meter?
Hard
- A1.5 V
- B0.15 V
- C1500 V
- D4.2 V
30.A battery of four identical cells, each with emf ε = 0.70 V, is connected in series with a fixed resistor R = 0.62 kΩ. A current I = 4.50 mA travels through the circuit. What is the emf of the battery?
Hard
- A0.70 V
- B2.80 V
- C1.40 V
- D0.18 V
31.A 1.5 V battery is connected to a circuit drawing 2.0 A. On a graph of terminal voltage against time, which change is observed when the circuit is altered to draw only 1.0 A?
Medium
- AThe terminal voltage falls more slowly and stays higher
- BThe terminal voltage falls more quickly and drops lower
- CThe terminal voltage remains constant at 1.5 V
- DThe terminal voltage rises above 1.5 V
32.A current I = 10 A flows through a network of six resistors. The potential difference across the line XY is 8 V. Which of the following statements are correct? (select all that apply)
Hard
- AThe resistance between X and Y is 0.8 Ω
- BThe resistance between X and Y is 1.25 Ω
- CThe value of the unknown resistance R can be found using R = V/I
- DThe unknown resistance R is 8 Ω
- EThe current through each resistor is 10 A
33.A variable resistor R with resistance varying between 0 and 10 Ω is connected in series with a fixed resistor and a battery. As the resistance of the variable resistor is increased, what happens to the current in the circuit?
Medium
- AThe current increases
- BThe current decreases
- CThe current stays the same
- DThe current first increases then decreases
34.In a circuit, a current of 2.0 A flows through a resistor for 90 minutes. What is the total charge that passes through the resistor?
Medium
- A180 C
- B10 800 C
- C1.8 C
- D108 C
35.A student is investigating the electrical resistivity of a resistor made from a thin film of carbon. A potential difference of 2.5 mV is applied across the resistor. The resistivity of carbon is 4.1 × 10⁻⁵ Ω m. The film has a length of 0.5 m and a cross-sectional area of 2.0 × 10⁻⁶ m². Calculate the current which passes through the carbon film.
Medium
- A2.4 × 10⁻⁴ A
- B2.4 × 10⁻³ A
- C0.16 A
- D1.6 A
36.A carbon film resistor has a length of 5.0 mm, a cross-sectional area of 2.0 × 10⁻⁸ m² and a resistivity of 4.1 × 10⁻⁵ Ω m. A potential difference of 2.5 mV is applied across it. What is the current through the film?
Medium
- A0.00024 A
- B0.024 A
- C2.4 A
- D0.0024 A
37.A carbon film resistor has a length of 5.0 mm, a cross-sectional area of 2.0 × 10⁻⁶ m² and a resistivity of 4.1 × 10⁻⁵ Ω m. A potential difference of 2.5 mV is applied across it. What is the current through the film?
Medium
- A0.024 A
- B0.24 A
- C2.4 A
- D0.0024 A
38.A current of 10 A flows through a resistor network, and the potential difference across it is 8 V. The network is an unknown resistor R in parallel with a 2 Ω resistor, with this combination in series with a 0.5 Ω resistor. What is the value of R?
Medium
- A0.35 Ω
- B0.8 Ω
- C1.25 Ω
- D0.5 Ω
39.A current I = 10 A flows through a network. The potential difference across the line XY is 8 V. The network consists of a resistor R in parallel with a 2 Ω resistor, and this combination is in series with a 0.5 Ω resistor. What is the value of the unknown resistance R?
Medium
- A0.35 Ω
- B0.8 Ω
- C1.25 Ω
- D2.0 Ω
40.A network is comprised of four identical resistors each of resistance 2 Ω connected to a 6 V battery with negligible internal resistance. If the resistors are connected in a combination of two in series and two in parallel, determine the reading on the ammeter.
Medium
- A3 A
- B6 A
- C1.5 A
- D12 A
41.State the definition of the coulomb.
Medium
42.A charge of 15.0 C passes through a resistor at a constant rate in 60 s. The potential difference across the resistor is 2.0 V. Calculate the resistance of the resistor.
Medium
43.Complete the sentence about the resistivity equation.
Medium
The resistivity ρ of a material is given by ρ = ____ / ____, where R is resistance, A is cross-sectional area and L is length.
44.A current of 2.0 A flows through a resistor for 90 minutes. Calculate the total charge that passes through the resistor.
Medium
45.A battery of emf 7.3 V and internal resistance 0.3 Ω is connected in series with a resistor of resistance 9.5 Ω. Calculate the current in the circuit in amperes, to 2 significant figures.
Medium
46.A copper wire has a resistivity of 1.7 × 10⁻⁸ Ω m, a diameter of 2.0 mm and a length of 20 mm. Calculate the resistance of the wire in ohms, to 2 significant figures.
Medium
47.Complete the sentence about the equation for resistivity.
Easy
The resistivity ρ of a material is given by ρ = ____ / ____, where R is resistance, A is cross-sectional area, and L is length.
48.What is the name of the component whose resistance decreases as light intensity increases?
Medium
49.A charge of 60 μC flows through a conductor in 140 ms. Calculate the current in the conductor, in mA.
Medium
50.An electrically-conducting wire is made from copper. The resistivity of copper is 1.7 × 10⁻⁸ Ω m, the diameter of the wire is 2.0 mm and the length of the wire is 20 mm. Calculate the cross-sectional area of the wire in m², to 2 significant figures.
Medium
51.Using the same copper wire (resistivity 1.7 × 10⁻⁸ Ω m, diameter 2.0 mm, length 20 mm), calculate the resistance of the wire in ohms, to 2 significant figures.
Hard
52.The internal resistance of the cell in the previous circuit is 1.3 kΩ. Calculate the emf of the cell in volts.
Hard
53.Explain why an ideal ammeter should have zero resistance.
Medium
54.Explain why the reading on a voltmeter connected across the terminals of a battery decreases when the switch in the circuit is closed.
Medium
55.Explain, with reference to charge carriers, why there is a current detected in a copper wire when a potential difference is applied across it.
Medium
56.State and explain why knowledge of quantities such as resistivity is useful to scientists.
Hard
57.A charge of 15.0 C passes through a resistor at a constant rate in 60 s. The potential difference across the resistor is 2.0 V. Calculate the resistance of the resistor.
Medium
- A10 Ω
- B9 Ω
- C8 Ω
- D7 Ω
58.A current of 2.0 A flows through a resistor for 90 minutes. Calculate the total charge that passes through the resistor.
Medium
- A12960 C
- B9720 C
- C10800 C
- D11880 C
59.A battery of emf 7.3 V and internal resistance 0.3 Ω is connected in series with a resistor of resistance 9.5 Ω. Calculate the current in the circuit in amperes, to 2 significant figures.
Medium
- A0.74 A
- B-0.26 A
- C1.74 A
- D2.74 A
60.A copper wire has a resistivity of 1.7 × 10⁻⁸ Ω m, a diameter of 2.0 mm and a length of 20 mm. Calculate the resistance of the wire in ohms, to 2 significant figures.
Medium
- A0.00011 Ω
- B-0.9999 Ω
- C1.0001 Ω
- D2.0001 Ω
61.A charge of 60 μC flows through a conductor in 140 ms. Calculate the current in the conductor, in mA.
Medium
- A-0.57 mA
- B1.43 mA
- C0.43 mA
- D2.43 mA
62.An electrically-conducting wire is made from copper. The resistivity of copper is 1.7 × 10⁻⁸ Ω m, the diameter of the wire is 2.0 mm and the length of the wire is 20 mm. Calculate the cross-sectional area of the wire in m², to 2 significant figures.
Medium
- A0.0000031 m²
- B2 m²
- C-1 m²
- D1 m²
63.Using the same copper wire (resistivity 1.7 × 10⁻⁸ Ω m, diameter 2.0 mm, length 20 mm), calculate the resistance of the wire in ohms, to 2 significant figures.
Hard
- A1.0001 Ω
- B2.0001 Ω
- C-0.9999 Ω
- D0.00011 Ω
64.The internal resistance of the cell in the previous circuit is 1.3 kΩ. Calculate the emf of the cell in volts.
Hard
- A2.28 V
- B3.28 V
- C4.28 V
- D1.28 V

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