Series and parallel circuits

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レッスンノート

Series Circuits

A series circuit has components connected end to end in a single loop.
The current is the same at all points in a series circuit.
The total potential difference of the power supply is shared between the components.
The total resistance is the sum of the individual resistances: R = R₁ + R₂ + R₃ ...
Adding more resistors in series increases the overall resistance because charge must pass through more components.
If one component breaks, the whole circuit stops working, and components cannot be controlled separately.

A simple series circuit

Parallel Circuits

A parallel circuit has components connected on separate branches.
The potential difference across each component is the same.
The total current from the supply is the sum of the currents through the separate branches.
The total resistance of two resistors in parallel is less than the resistance of the smallest individual resistor.
Adding more resistors in parallel decreases the overall resistance because each resistor provides an extra path for charge to flow.
Components can be controlled individually, and if one stops working, the others continue to function.

Potential difference in a parallel circuit

Comparing Series and Parallel Circuits

In series, current is the same everywhere; in parallel, current splits at junctions.
In series, potential difference is shared; in parallel, potential difference is the same across each branch.
In series, total resistance increases with more components; in parallel, total resistance decreases.
The current in each parallel branch is only identical if the resistance of each branch is identical.
Some circuits include both series and parallel parts.

Calculation of current splitting at a junction in a parallel circuit

Resistors in Series and Parallel

For resistors in series, the combined resistance is the sum of individual resistances.
For resistors in parallel, the combined resistance is less than the smallest individual resistance.
In parallel, each resistor creates an extra path for charge, allowing more charge to flow overall and reducing resistance.
Increasing the number of resistors in series increases resistance because charge has more components to pass through.
In a series circuit, the total voltage is the sum of the voltages across each component.

Electrical Components and I-V Graphs

Fixed resistors: current is directly proportional to potential difference; the I-V graph is a straight line through the origin.
Filament lamps: resistance increases as temperature increases; the I-V graph curves, showing current increasing at a slower rate.
Diodes: allow current in one direction only (forward bias); in reverse bias, resistance is very high and no current flows.
LDRs: resistance decreases as light intensity increases.
Thermistors: resistance decreases as temperature increases.
LDRs and thermistors are sensory resistors used in light sensors and temperature sensors.

Testing Components

To investigate resistance variation, use a circuit with an ammeter in series and a voltmeter in parallel with the component.
A variable resistor changes the current through the component.
For filament lamps and diodes, vary current and measure voltage; calculate resistance using R = V/I.
For LDRs, vary light intensity; for thermistors, vary temperature; record voltage and current to calculate resistance.
Ensure the component is connected to a low voltage supply (below 15 V) to avoid overheating.
Wait a few seconds before taking readings to allow the component to react.

Core Practical: Investigating Circuits

Investigate the relationship between potential difference, current and resistance for a resistor and a filament lamp.
Vary voltage using a variable resistor and record current for each voltage; take multiple readings and calculate averages.
Switch off the circuit between readings to prevent heating.
Plot an I-V graph: straight line through origin for fixed resistor; curve for filament lamp.
Test series and parallel circuits: measure voltage and current, calculate resistance.
In series, total resistance is the sum of individual resistances; in parallel, total resistance is less than either individual resistance.

AC and DC

Direct current (d.c.): current flows steadily in one direction; cells and batteries produce d.c.
Alternating current (a.c.): current continuously changes direction; mains electricity is a.c.
In the UK, mains electricity has a frequency of 50 Hz and a potential difference of about 230 V.
A.c. is represented by a sine wave on an oscilloscope; d.c. is a straight line.
A d.c. power supply has fixed positive and negative terminals; an a.c. supply has two identical terminals.

Mains Electricity and Safety

Mains electricity is an a.c. supply with live, neutral and earth wires.
Live wire (brown) carries the alternating potential difference; it is the most dangerous.
Neutral wire (blue) completes the circuit and is close to 0 V.
Earth wire (green and yellow stripes) is a safety wire that prevents the appliance from becoming live.
If a fault occurs, the earth wire provides a low resistance path, causing a surge of current that melts the fuse and cuts off the supply.
The live wire has a potential difference of about 230 V, so contact can be lethal.

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練習問題

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1.In a series circuit, how does the current at one point compare with the current at another point?
Easy
- AThe current is the same at all points
- BThe current is larger near the power supply
- CThe current splits between the components
- DThe current is smaller after each component
2.In a parallel circuit, what happens to the current at a junction?
Easy
- AIt splits into the separate branches
- BIt stays the same in every branch
- CIt is destroyed at the junction
- DIt is shared equally whatever the resistances are
3.A 12 V battery is connected to two identical lamps in series. What is the potential difference across each lamp?
Easy
- A12 V
- B6 V
- C24 V
- D0 V
4.A 12 V battery is connected to two identical lamps in parallel. What is the potential difference across each lamp?
Easy
- A12 V
- B6 V
- C24 V
- D0 V
5.Which statement about the total resistance of two resistors in parallel is correct?
Medium
- AIt is less than the resistance of the smallest individual resistor
- BIt is the sum of the two resistances
- CIt is greater than either individual resistance
- DIt is equal to the larger of the two resistances
6.Which of the following are true for components connected in series? (select all that apply)
Medium
- AThe current is the same through each component
- BThe total potential difference of the supply is shared between the components
- CThe total resistance is the sum of the individual resistances
- DThe potential difference is the same across each component
- EThe current splits between the components
7.Which of the following are true for components connected in parallel? (select all that apply)
Medium
- AThe potential difference across each component is the same
- BThe total current is the sum of the currents through the separate components
- CThe total resistance is less than the resistance of the smallest individual resistor
- DThe current is the same through each component
- EThe total resistance is the sum of the individual resistances
8.In a series circuit, the potential difference of the power supply is shared between the components.
Easy
True or false?

もっと問題

9.Adding more resistors in parallel increases the total resistance of the circuit.
Easy
True or false?
10.In a parallel circuit, the current in each branch is always identical.
Easy
True or false?
11.If one component in a series circuit breaks, the other components stop working.
Medium
True or false?
12.If one component in a parallel circuit stops working, the other components continue to function.
Medium
True or false?
13.Match each quantity in a series circuit to how it behaves.
Medium
- Current
- Potential difference of the supply
- Total resistance
- The same at all points
- Shared between the components
- The sum of the individual resistances
14.Match each quantity in a parallel circuit to how it behaves.
Medium
- Potential difference across each component
- Total current
- Total resistance
- The same across each component
- The sum of the currents in the separate branches
- Less than the resistance of the smallest individual resistor
15.Arrange the steps to find the total resistance of two resistors connected in series.
Easy
- Identify the resistance of each resistor
- Add the individual resistances together
- Write down the total resistance with the unit Ω
16.How does the total resistance of the two resistors in series compare with the total resistance of the same two resistors in parallel?
Medium
- AThe series total is larger than the parallel total
- BThe series total is smaller than the parallel total
- CThe two totals are equal
- DIt is impossible to compare them without knowing the resistance values
17.In the parallel arrangement, the current from the battery is larger than the current in each individual branch.
Medium
True or false?
18.Which of the following statements about a series circuit are correct? (select all that apply)
Medium
- AThe current is the same at every point in the circuit
- BThe potential difference of the power supply is shared between the components
- CThe total resistance is the sum of the individual resistances
- DThe potential difference across each component is the same
- EThe current splits at junctions between components
19.Which of the following statements about a parallel circuit are correct? (select all that apply)
Medium
- AThe potential difference across each branch is the same
- BThe total current from the supply is the sum of the currents in the branches
- CThe total resistance is less than the resistance of the smallest individual resistor
- DThe current is the same in every branch
- EThe total resistance is the sum of the individual resistances
20.Match each circuit quantity to the correct statement for a series circuit.
Medium
- Current
- Potential difference
- Total resistance
- Same at all points
- Shared between components
- Sum of individual resistances
21.Match each circuit quantity to the correct statement for a parallel circuit.
Medium
- Current
- Potential difference
- Total resistance
- Splits at junctions and adds up to the supply current
- Same across each branch
- Less than the smallest individual resistance
22.Arrange these steps in the correct order to measure the total resistance of two resistors connected in parallel.
Medium
- Record the voltmeter reading across the parallel combination
- Set up the two resistors in parallel with a cell, ammeter and voltmeter
- Calculate total resistance using R = V / I
- Record the ammeter reading for the total current from the cell
23.Arrange these steps in the correct order to find the combined resistance of two resistors connected in series.
Medium
- Identify the resistance of each resistor
- Use R = R1 + R2
- Add the two resistance values
- State the combined resistance with the unit ohms
24.In a series circuit, what is the relationship between the current through the power supply and the current through each component?
Easy
- AThe current is the same through every component
- BThe current is shared equally between components
- CThe current is larger through the first component
- DThe current is smaller through the last component
25.In a parallel circuit, how does the current from the power supply compare with the current in each branch?
Easy
- AThe supply current is larger than the current in each branch
- BThe supply current is smaller than the current in each branch
- CThe supply current is equal to the current in each branch
- DThe supply current is zero
26.Which of the following are advantages of connecting components in parallel rather than in series? (select all that apply)
Medium
- AComponents can be switched on and off individually
- BIf one component stops working, the others continue to function
- CThe total resistance is less than the resistance of the smallest component
- DThe current is the same through every component
- EThe potential difference is shared between components
27.In a parallel circuit, the potential difference across each branch is the same.
Easy
True or false?
28.Adding more resistors in series decreases the total resistance of the circuit.
Easy
True or false?
29.A circuit has two resistors connected in parallel. The current through the first resistor is 0.5 A and through the second is 0.3 A. What is the current from the power supply?
Medium
- A0.8 A
- B0.2 A
- C0.15 A
- D0.5 A
30.A 12 V battery is connected to a series circuit containing a 4 Ω resistor and a 2 Ω resistor. What is the potential difference across the 4 Ω resistor?
Medium
- A8 V
- B4 V
- C6 V
- D12 V
31.A 6 V battery is connected to two identical lamps in parallel. What is the potential difference across each lamp?
Medium
- A6 V
- B3 V
- C12 V
- D0 V
32.Which of the following are true about a series circuit? (select all that apply)
Medium
- AThe current is the same at all points
- BThe total resistance is the sum of the individual resistances
- CThe potential difference is shared between components
- DThe current splits at junctions
- EThe total resistance is less than the smallest resistance
33.The graphs below show how the current in a component changes with the voltage applied across it. Which component has an I–V graph that is a straight line through the origin?
Medium
- AFixed resistor
- BFilament lamp
- CDiode
- DThermistor
34.Which of the following is a non-ohmic conductor?
Medium
- ADiode
- BFixed resistor
- CCopper wire
- DAmmeter
35.Which of the following is true about resistors in series and parallel?
Medium
- AIf two resistors are in series, their net resistance is decreased
- BIf two resistors are in parallel, their net resistance is increased
- CIf two resistors are in series or parallel, their net resistance is increased
- DIf two resistors are in parallel, their net resistance is decreased
36.A student investigates how the overall resistance of a circuit changes when additional identical resistors are added in parallel. The results show that as more resistors are added, the overall resistance decreases. Which statement explains this?
Medium
- AEach resistor adds more paths for charge to flow, so the total current increases and overall resistance decreases.
- BThe resistors share the current equally, so the total resistance is the average of the individual resistances.
- CAdding resistors in parallel increases the total resistance because there are more components.
- DThe potential difference across each resistor increases, which reduces the resistance.
37.A circuit contains a battery, a fixed resistor, and a filament lamp connected in series. Which of the following statements are correct? (select all that apply)
Hard
- AThe current through the resistor is the same as the current through the lamp.
- BThe potential difference across the resistor is the same as the potential difference across the lamp.
- CThe total resistance of the circuit is the sum of the resistance of the resistor and the lamp.
- DThe potential difference of the battery is shared between the resistor and the lamp.
- EThe current splits at the junction between the resistor and the lamp.
38.In a parallel circuit, the total current from the power supply is equal to the current in each branch.
Easy
True or false?
39.Match each circuit quantity with its correct behaviour in a series circuit.
Medium
- Current
- Potential difference
- Total resistance
- Same at all points
- Shared between components
- Sum of individual resistances
40.Arrange the steps in the correct order to test series and parallel circuits using two fixed resistors.
Medium
- Set up the circuit with a single fixed resistor.
- Record the voltage using the voltmeter and the current using the ammeter.
- Calculate the resistance for each pair of voltage and current readings.
- Arrange the two resistors in series and repeat the measurements.
- Arrange the two resistors in parallel and repeat the measurements.
41.Two resistors of 30 Ω and 10 Ω are connected in series. Calculate the total resistance of the two resistors.
Medium
42.A series circuit has a combined resistance of 60 Ω. It contains a 30 Ω resistor, an unknown resistor and a 10 Ω resistor. Calculate the resistance of the unknown resistor.
Medium
43.A cell supplies a current of 2 A to a series circuit containing a fixed resistor of resistance 4 Ω. Calculate the potential difference across the resistor.
Medium
44.Complete the sentence about a series circuit.
Easy
In a series circuit, the current is the ____ at all points, and the total potential difference of the power supply is ____ between the components.
45.Complete the sentence about a parallel circuit.
Easy
In a parallel circuit, the potential difference across each component is the ____, and the total current is the ____ of the currents through the separate components.
46.Complete the sentence about the current in a parallel circuit.
Easy
In a parallel circuit, the current ____ at junctions, some going one way and the rest going the other.
47.State the name of the point in a parallel circuit where the current splits into separate branches.
Easy
48.State the term for the combined resistance of all the components in a circuit.
Easy
49.Two resistors of 6 Ω and 3 Ω are connected in series. Calculate the total resistance.
Medium
50.A series circuit has a total resistance of 50 Ω and contains a 20 Ω resistor and a 10 Ω resistor. Calculate the resistance of the third resistor.
Medium
51.A 12 V battery is connected to three identical lamps in parallel. Calculate the potential difference across each lamp.
Medium
52.A series circuit contains a 4 Ω resistor and a 2 Ω resistor. The current through the circuit is 0.5 A. Calculate the potential difference across the 4 Ω resistor.
Medium
53.Explain why adding a resistor in parallel decreases the total resistance of a circuit.
Medium
54.Describe the difference between a series circuit and a parallel circuit in terms of how the current and potential difference behave.
Medium
55.Two resistors of 30 Ω and 10 Ω are connected in series. Calculate the total resistance of the two resistors.
Medium
- A44 Ω
- B40 Ω
- C48 Ω
- D36 Ω
56.A series circuit has a combined resistance of 60 Ω. It contains a 30 Ω resistor, an unknown resistor and a 10 Ω resistor. Calculate the resistance of the unknown resistor.
Medium
- A24 Ω
- B18 Ω
- C20 Ω
- D22 Ω
57.A cell supplies a current of 2 A to a series circuit containing a fixed resistor of resistance 4 Ω. Calculate the potential difference across the resistor.
Medium
- A8 V
- B7 V
- C9 V
- D10 V
58.Two resistors of 6 Ω and 3 Ω are connected in series. Calculate the total resistance.
Medium
- A9 Ω
- B10 Ω
- C11 Ω
- D8 Ω
59.A series circuit has a total resistance of 50 Ω and contains a 20 Ω resistor and a 10 Ω resistor. Calculate the resistance of the third resistor.
Medium
- A20 Ω
- B22 Ω
- C18 Ω
- D24 Ω
60.A 12 V battery is connected to three identical lamps in parallel. Calculate the potential difference across each lamp.
Medium
- A13 V
- B12 V
- C14 V
- D11 V
61.A series circuit contains a 4 Ω resistor and a 2 Ω resistor. The current through the circuit is 0.5 A. Calculate the potential difference across the 4 Ω resistor.
Medium
- A3 V
- B1 V
- C4 V
- D2 V

フラッシュカード

What is a series circuit?

A circuit where components are connected end to end in a single loop, so the current flows through each component in turn.

What is a parallel circuit?

A circuit where components are connected along separate branches, so the current has more than one path to flow through.

In a series circuit, how does the current behave at different points?

The current is the same at all points in the circuit, so it is the same through each component.

In a series circuit, how is the potential difference of the power supply distributed?

The total potential difference of the power supply is shared between the components.

How do you calculate the total resistance of resistors in series?

Add the individual resistances together: R = R₁ + R₂ + R₃ ...

Why does adding more resistors in series increase the total resistance?

The charge has to pass through more components, so there are more collisions and it is harder for charge to flow.

In a parallel circuit, how does the potential difference compare across each component?

The potential difference across each component is the same.

In a parallel circuit, how does the total current relate to the branch currents?

The total current through the whole circuit is the sum of the currents through the separate branches: I = I₁ + I₂.

How does the total resistance of two resistors in parallel compare with the smallest individual resistor?

The total resistance is less than the resistance of the smallest individual resistor.

Why does adding a resistor in parallel decrease the total resistance?

Each resistor creates an extra path for charge to flow, so more charge flows overall and the overall resistance is smaller.

Why does the current split unequally between branches of a parallel circuit?

The current in each branch is only identical if the resistance along each branch is identical; more current flows in the branch with less resistance.

Why must the total current be conserved around a circuit?

Current is the flow of electrons, which cannot be created or destroyed, so the total number of electrons going around the circuit stays the same.

What happens to the current at a junction in a parallel circuit?

The current splits at the junction, with some electrons going one way and the rest going the other way.

Give two disadvantages of connecting components in series.

If one component breaks, all the others stop working, and the components cannot be controlled (switched on and off) separately.

Give two advantages of connecting components in parallel.

Components can be individually controlled using their own switches, and if one component stops working the others continue to function.

What is an ohmic conductor?

A conductor that has a fixed (constant) resistance, so current is directly proportional to potential difference.

Which of these are non-ohmic conductors: diode, thermistor, filament lamp, LDR, resistor?

Diode, thermistor, filament lamp and LDR are non-ohmic; a fixed resistor is ohmic.

What does the I–V graph of a fixed resistor look like?

A straight line passing through the origin, showing current is directly proportional to potential difference.

Why is the I–V graph of a filament lamp curved?

As current increases the filament temperature rises, making atoms vibrate more, which increases resistance so current increases at a slower rate.

How does the resistance of a filament lamp change as its temperature increases?

The resistance increases as the temperature of the filament increases.

How does a diode behave in forward and reverse bias?

In forward bias it allows current to flow in one direction; in reverse bias it has very high resistance so no current flows.

How does the resistance of an LDR vary with light intensity?

As light intensity increases the resistance of the LDR decreases, and vice versa.

How does the resistance of a thermistor vary with temperature?

As temperature increases the resistance of the thermistor decreases, and vice versa.

What is the circuit symbol for an LDR?

A resistor symbol (a rectangle) with arrows pointing towards it, representing light falling on it.

What is the circuit symbol for a thermistor?

A resistor symbol (a rectangle) with a diagonal line through it that has a horizontal line at its base.

What is the circuit symbol for an LED?

A diode symbol (a triangle pointing at a line) with two small arrows pointing away from it to show light emitted.

Where is the ammeter connected in a circuit and why?

In series with the component, because it measures the current flowing through that component.

Where is the voltmeter connected in a circuit and why?

In parallel with the component, because it measures the potential difference across that component.

What is the purpose of a variable resistor in an investigation of a component?

It is used to change the current flowing through the component so a range of readings can be taken.

How is the resistance of a component calculated from current and voltage readings?

Using R = V ÷ I, where V is the potential difference and I is the current.

What does the gradient of a current–potential difference graph represent?

The gradient represents 1 ÷ resistance (the reciprocal of resistance).

Why should the power supply be switched off between readings in a circuit investigation?

To prevent the components and wires from heating up, which would change their resistance.

Why should a low voltage (below 15 V) be used when testing a component?

A high current would heat the component and affect its resistance, giving invalid results.

What is direct current (d.c.)?

A current that is steady and constantly flows in the same direction around a circuit, from positive to negative.

What is alternating current (a.c.)?

A current that continuously changes direction, going back and forth around a circuit.

What is the frequency and potential difference of UK mains electricity?

A frequency of 50 Hz and a potential difference of about 230 V.

What does a frequency of 50 Hz mean for mains electricity?

The direction of the current changes back and forth 50 times every second.

What are the colours of the live, neutral and earth wires in a three-core cable?

Live is brown, neutral is blue, and earth is green and yellow stripes.

What is the purpose of the live wire?

It carries the alternating potential difference from the mains supply to the circuit, and is the most dangerous wire.

What is the purpose of the neutral wire?

It forms the opposite end of the circuit to the live wire, completing the circuit, and is much less dangerous.

What is the purpose of the earth wire?

It is a safety wire that stops the appliance from becoming live, preventing electric shocks if a fault occurs.

How does the earth wire protect a user if a live wire touches a metal case?

It provides a low-resistance path to earth, causing a surge of current that melts the fuse and cuts off the supply.

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