Cambridge IGCSE0972

Electric circuits

Physics 0972 Chapter Notes

What this chapter covers

Electric circuits - Circuit diagrams and circuit componentsElectric circuits - Series and parallel circuitsElectric circuits - Action and use of circuit components
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In this chapter

  1. 1Circuit Basics and Symbols
  2. 2Series Circuits
  3. 3Parallel Circuits
  4. 4Calculating Total Resistance
  5. 5Potential Divider Circuits (Extended)
  6. 6Diodes and LEDs (Extended)

1. Circuit Basics and Symbols

An electric circuit is a complete path for electric current to flow. For current to flow, there must be a source of potential difference (like a battery) and an unbroken loop of conducting material (like copper wire). We use standard symbols to draw circuits neatly. Key quantities are: Current (I), the flow of charge, measured in Amperes (A); Potential Difference (p.d. or V), the 'push' given to the charge, measured in Volts (V); and Resistance (R), how much a component opposes the current, measured in Ohms (Ω). To measure current, an ammeter is connected in series (in the loop). To measure p.d., a voltmeter is connected in parallel (across the component).

V = I × R

Key term

Electric Circuit: A complete, unbroken path around which electric charge can flow.

Examiner insight

Examiners award marks for correctly drawn circuit diagrams using standard symbols and for placing ammeters in series and voltmeters in parallel.

Common pitfall

Connecting a voltmeter in series or an ammeter in parallel. This is a fundamental error that shows a misunderstanding of how these meters work.

Fun fact

The standard symbols used in circuit diagrams are internationally agreed, allowing engineers worldwide to understand each other's designs without a language barrier.

Worked example 14 marks

A lamp with a resistance of 6.0 Ω is connected to a 12 V battery. Draw the circuit diagram including a switch, an ammeter to measure the current through the lamp, and a voltmeter to measure the p.d. across the lamp. Calculate the current flowing through the lamp when the switch is closed.

  1. 1

    Step 1: Draw the circuit. A cell or battery symbol connected by lines to a switch symbol, a lamp symbol, and an ammeter symbol (circle with 'A'), all in a single loop. Draw a voltmeter symbol (circle with 'V') connected with lines on either side of the lamp.

  2. 2

    Step 2: State the relevant formula. Ohm's Law: V = I × R.

  3. 3

    Step 3: Rearrange the formula to find the current, I. I = V / R.

  4. 4

    Step 4: Substitute the known values into the formula. I = 12 V / 6.0 Ω.

  5. 5

    Step 5: Calculate the result. I = 2.0 A. The current flowing through the lamp is 2.0 A.

Recap

  • A circuit must be a complete, closed loop for current to flow.
  • Current (I) is measured in Amperes (A) with an ammeter placed in series.
  • Potential difference (V) is measured in Volts (V) with a voltmeter placed in parallel.
  • Resistance (R) is measured in Ohms (Ω).
  • Ohm's Law, V = I × R, links the three key quantities.

Quick check

  1. What is the correct way to connect a voltmeter to measure the p.d. across a resistor?1 mark
  2. An ammeter reads 0.5 A and the p.d. across a component is 3.0 V. What is its resistance?2 marks

2. Series Circuits

In a series circuit, components are connected one after another in a single, unbranched loop. If you imagine the current as cars on a one-lane road, they all have to follow the same path. This means the current is the same at every point in a series circuit. The total potential difference from the supply (e.g., a battery) is shared between the components. The total resistance of the circuit is found by simply adding up the resistance of each component.

I_total = I_1 = I_2 = ...

V_supply = V_1 + V_2 + ...

R_total = R_1 + R_2 + ...

Key term

Series Circuit: A circuit where components are connected end-to-end in a single loop, providing only one path for the current.

Examiner insight

Marks are often awarded for clearly stating that the current is the same at all points in a series circuit, as this is a fundamental rule.

Common pitfall

Incorrectly assuming the voltage is the same across each component in a series circuit. Remember, voltage is shared, not equal.

Fun fact

Old-fashioned Christmas tree lights were often wired in series. If one bulb failed, it broke the circuit and the entire string of lights would go out, leading to a frustrating search for the single faulty bulb!

Worked example 15 marks

Two resistors, R1 = 4.0 Ω and R2 = 8.0 Ω, are connected in series with a 6.0 V battery. Calculate:(a) the total resistance of the circuit,(b) the current flowing from the battery, and(c) the potential difference across the 8.0 Ω resistor.

  1. 1

    Part (a): Total resistance in series is the sum of individual resistances.

  2. 2

    R_total = R_1 + R_2 = 4.0 Ω + 8.0 Ω = 12.0 Ω.

  3. 3

    Part (b): Use Ohm's law for the whole circuit. I = V_supply / R_total.

  4. 4

    I = 6.0 V / 12.0 Ω = 0.50 A. This is the current at all points in the circuit.

  5. 5

    Part (c): Use Ohm's law for the 8.0 Ω resistor. The current through it is 0.50 A.

  6. 6

    V_2 = I × R_2 = 0.50 A × 8.0 Ω = 4.0 V.

Recap

  • A series circuit provides only one path for the current.
  • The current is the same at every point in a series circuit.
  • The supply voltage is shared between the components.
  • Total resistance is the sum of the individual resistances (R_total = R_1 + R_2).
  • If one component breaks in a series circuit, the entire circuit stops working.

Quick check

  1. If three lamps are in series and the current through the first lamp is 0.2 A, what is the current through the third lamp?1 mark
  2. What is the total resistance of a 10 Ω, 20 Ω and 30 Ω resistor connected in series?1 mark

3. Parallel Circuits

In a parallel circuit, components are connected in separate branches. The circuit splits, allowing the current to follow multiple paths. Think of it like a river splitting into several streams and then rejoining. The key rules are: The potential difference (voltage) across each parallel branch is the same as the supply voltage. The total current flowing from the supply is the sum of the currents in each individual branch. This is a huge advantage, as components can be switched on and off independently, and each gets the full supply voltage. This is how your home is wired.

V_supply = V_1 = V_2 = ...

I_total = I_1 + I_2 + ...

Key term

Parallel Circuit: A circuit that contains two or more branches for current to flow through.

Examiner insight

Examiners look for the understanding that connecting components in parallel allows them to be switched independently and that each receives the full supply voltage.

Common pitfall

Assuming the current is the same in each parallel branch. It is only the same if the resistance of each branch is identical.

Fun fact

The wiring in your house is a large parallel circuit. This allows you to turn on a light in one room without having to turn on every single appliance in the house at the same time.

Worked example 14 marks

A 12 Ω resistor and a 6 Ω resistor are connected in parallel to a 6 V battery.(a) What is the potential difference across each resistor?(b) Calculate the current in each resistor.(c) What is the total current drawn from the battery?

  1. 1

    Part (a): In a parallel circuit, the p.d. across each branch is the same as the supply p.d. So, the p.d. across both the 12 Ω and 6 Ω resistors is 6 V.

  2. 2

    Part (b): Calculate current for the 12 Ω resistor using I = V/R. I_1 = 6 V / 12 Ω = 0.5 A.

  3. 3

    Calculate current for the 6 Ω resistor using I = V/R. I_2 = 6 V / 6 Ω = 1.0 A.

  4. 4

    Part (c): The total current is the sum of the branch currents.

  5. 5

    I_total = I_1 + I_2 = 0.5 A + 1.0 A = 1.5 A.

Recap

  • A parallel circuit provides multiple paths for the current.
  • The voltage is the same across all branches in a parallel circuit.
  • The total current is the sum of the currents in the individual branches.
  • Components in parallel can be operated independently.
  • If one component in a parallel branch breaks, the other branches continue to work.

Quick check

  1. If two lamps are connected in parallel to a 9 V battery, what is the voltage across each lamp?1 mark
  2. Why are lights in a house wired in parallel and not in series?2 marks

4. Calculating Total Resistance

The total resistance of a circuit is often called the equivalent resistance. For a series circuit, it's simple: you just add the individual resistances. For a parallel circuit, the calculation is different. Adding a resistor in parallel provides another path for the current, so the total resistance actually decreases. The total resistance in a parallel circuit is always less than the smallest individual resistor in any of the branches. The formula involves reciprocals, so be careful with your calculator work.

R_total = R_1 + R_2 + ... (Series)

1/R_total = 1/R_1 + 1/R_2 + ... (Parallel)

R_total = (R_1 × R_2) / (R_1 + R_2) (For two resistors in parallel)

Key term

Equivalent Resistance: The single resistance value that would have the same effect as all the individual resistors in a circuit or part of a circuit.

Examiner insight

For parallel resistance calculations, full marks require showing the '1/R' formula, correct substitution, and the final inversion step. Simply stating the answer is not enough.

Common pitfall

Forgetting to take the reciprocal at the end of a parallel resistance calculation. For example, calculating 1/R_total = 0.25 and giving the answer as 0.25 Ω instead of R_total = 1/0.25 = 4.0 Ω.

Worked example 13 marks

Two resistors, a 10 Ω and a 15 Ω, are connected in parallel. Calculate their combined resistance.

  1. 1

    Step 1: State the formula for parallel resistance. 1/R_total = 1/R_1 + 1/R_2.

  2. 2

    Step 2: Substitute the values. 1/R_total = 1/10 + 1/15.

  3. 3

    Step 3: Find a common denominator to add the fractions. 1/R_total = 3/30 + 2/30 = 5/30.

  4. 4

    Step 4: Simplify the fraction. 1/R_total = 1/6.

  5. 5

    Step 5: Invert both sides to find R_total. R_total = 6/1 = 6 Ω.

  6. 6

    Alternatively, use the product-over-sum rule: R_total = (10 × 15) / (10 + 15) = 150 / 25 = 6 Ω.

Worked example 24 marks

Calculate the total resistance of the circuit shown: a 4 Ω resistor in series with a parallel combination of a 12 Ω and a 6 Ω resistor.

  1. 1

    Step 1: First, calculate the equivalent resistance of the parallel part (R_p).

  2. 2

    1/R_p = 1/12 + 1/6 = 1/12 + 2/12 = 3/12.

  3. 3

    R_p = 12/3 = 4 Ω.

  4. 4

    Step 2: The circuit is now equivalent to the 4 Ω series resistor and the 4 Ω equivalent resistance of the parallel part, both in series.

  5. 5

    Step 3: Calculate the total resistance by adding the series components.

  6. 6

    R_total = 4 Ω + R_p = 4 Ω + 4 Ω = 8 Ω.

Recap

  • In series, total resistance is the sum: R_total = R_1 + R_2.
  • In parallel, the reciprocal of total resistance is the sum of reciprocals: 1/R_total = 1/R_1 + 1/R_2.
  • For two resistors in parallel, the shortcut is R_total = (product) / (sum).
  • Adding a resistor in parallel always decreases the total resistance.

Quick check

  1. What is the total resistance of two 100 Ω resistors connected in parallel?2 marks

5. Potential Divider Circuits (Extended)

A potential divider is a simple and very useful circuit. It consists of two or more resistors connected in series to a supply voltage (V_in). The purpose is to 'tap off' a smaller voltage (V_out) from across one of the resistors. The output voltage depends on the ratio of the resistances. If the resistors are equal, the output voltage across one of them will be exactly half the input voltage. This principle is widely used in sensor circuits, where one of the resistors is a sensor like an LDR or thermistor, allowing the output voltage to change with light or temperature.

V_out = V_in × (R_2 / (R_1 + R_2))

Key term

Potential Divider: A circuit with several resistors in series used to provide a fraction of the total supply voltage as an output.

Examiner insight

Candidates score well when they can explain not just calculate, but also explain how changing the resistance of one component (like an LDR) affects the output voltage of a potential divider.

Common pitfall

Mixing up the resistors in the potential divider formula, for example, putting R1 in the numerator when calculating the voltage across R2.

Fun fact

The volume knob on many stereos is a variable resistor used as a potential divider. Turning the knob changes the resistance ratio, altering the output voltage (the audio signal) sent to the amplifier.

Worked example 13 marks

A potential divider is made by connecting a 10 kΩ and a 30 kΩ resistor in series to a 12 V supply. Calculate the output voltage taken across the 30 kΩ resistor.

  1. 1

    Step 1: Identify the components. V_in = 12 V, R_1 = 10 kΩ, R_2 = 30 kΩ. We want the voltage across R_2.

  2. 2

    Step 2: State the potential divider formula: V_out = V_in × (R_2 / (R_1 + R_2)).

  3. 3

    Step 3: Substitute the values into the formula. V_out = 12 V × (30 kΩ / (10 kΩ + 30 kΩ)).

  4. 4

    Step 4: Calculate the ratio of resistances. V_out = 12 V × (30 / 40) = 12 V × 0.75.

  5. 5

    Step 5: Calculate the final output voltage. V_out = 9.0 V.

Worked example 24 marks

A light-sensing circuit uses a Light Dependent Resistor (LDR) and a fixed 5 kΩ resistor in a potential divider connected to a 10 V supply. The LDR has a resistance of 1 kΩ in bright light and 20 kΩ in the dark. The output voltage is taken across the fixed resistor. Describe how the output voltage changes as it gets dark.

  1. 1

    Step 1: In bright light, R_LDR = 1 kΩ. The total resistance is 1 kΩ + 5 kΩ = 6 kΩ. The output voltage across the fixed resistor is V_out = 10 V × (5 kΩ / 6 kΩ) = 8.3 V.

  2. 2

    Step 2: In the dark, R_LDR = 20 kΩ. The total resistance is 20 kΩ + 5 kΩ = 25 kΩ. The output voltage across the fixed resistor is V_out = 10 V × (5 kΩ / 25 kΩ) = 2.0 V.

  3. 3

    Step 3: Conclude the change. As it gets dark, the resistance of the LDR increases. This means the LDR takes a larger share of the supply voltage, so the voltage across the fixed resistor decreases (from 8.3 V to 2.0 V).

Recap

  • A potential divider uses series resistors to produce a specific output voltage.
  • The output voltage is a fraction of the input voltage.
  • The formula is V_out = V_in × (R_out / R_total).
  • Potential dividers are used in sensor circuits with LDRs and thermistors.

Quick check

  1. In a potential divider with two identical resistors connected to a 10 V supply, what is the output voltage across one of them?1 mark

6. Diodes and LEDs (Extended)

A diode is a component that acts like a one-way street for current. It has a very low resistance when current flows in the 'forward' direction and a very high resistance in the 'reverse' direction. This means it effectively only allows conventional current to flow in the direction of its arrow symbol. A Light Emitting Diode (LED) is a special type of diode that emits light when current passes through it in the forward direction. Because LEDs are easily damaged by too much current, they must always be connected in series with a protective resistor to limit the current to a safe level.

Key term

Diode: A semiconductor component that allows electric current to pass in only one direction with very low resistance.

Examiner insight

Examiners expect students to know the correct symbol for a diode and to be able to identify from a diagram whether it is forward-biased (will conduct) or reverse-biased (will not conduct).

Common pitfall

Forgetting that a protective resistor is needed in series with an LED. Connecting an LED directly to a power supply will almost certainly destroy it.

Fun fact

LEDs are incredibly efficient. A 10-watt LED can produce the same amount of light as a 60-watt traditional incandescent bulb, saving a huge amount of energy.

Worked example 14 marks

An LED with a maximum safe current of 20 mA (0.020 A) is to be connected to a 5.0 V supply. The LED has a forward voltage drop of 2.0 V when lit.(a) Explain why a resistor must be used in series with the LED.(b) Calculate the resistance of the protective resistor needed.

  1. 1

    Part (a): A resistor must be used to limit the current flowing through the LED. Without it, the current from the 5.0 V supply would be too large and would destroy the LED.

  2. 2

    Part (b): First, find the voltage that must be dropped across the resistor. The supply is 5.0 V and the LED uses 2.0 V, so the resistor must have a p.d. of V_R = 5.0 V - 2.0 V = 3.0 V across it.

  3. 3

    Now use Ohm's law for the resistor. We want the current to be the maximum safe value, I = 0.020 A.

  4. 4

    R = V_R / I = 3.0 V / 0.020 A = 150 Ω.

  5. 5

    A 150 Ω resistor is needed.

Recap

  • A diode allows current to flow in one direction only.
  • The symbol for a diode is a triangle pointing towards a line, indicating the direction of conventional current.
  • An LED is a diode that emits light when current flows through it.
  • An LED must always be protected by a series resistor to limit the current.

Quick check

  1. Draw the circuit symbol for a Light Emitting Diode (LED).1 mark
  2. What happens if you connect a battery to a diode the wrong way round?1 mark

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. State the rules for the current and potential difference in (a) a series circuit and (b) a parallel circuit.4 marks
  2. A 3.0 Ω resistor and a 6.0 Ω resistor are connected in series with a 12 V battery. Calculate the total resistance and the current in the circuit.3 marks
  3. The same 3.0 Ω and 6.0 Ω resistors are now connected in parallel with the 12 V battery. Calculate (a) the total resistance and (b) the total current drawn from the battery.4 marks
  4. Explain two advantages of connecting lamps in a house in parallel rather than in series.2 marks
  5. A circuit contains a 10 V supply connected to a 20 Ω resistor and a 30 Ω resistor in series. A voltmeter is connected across the 30 Ω resistor. What reading will the voltmeter show?3 marks
  6. Draw a diagram of a circuit that could be used to investigate how the current through a resistor changes as the potential difference across it is varied. Your diagram must include a variable power supply, a resistor, an ammeter and a voltmeter.3 marks
  7. A student builds a potential divider using a 4 kΩ resistor and an 8 kΩ resistor, connected to a 9 V supply. Calculate the output voltage if it is taken across the 8 kΩ resistor.3 marks
  8. A circuit consists of a 10 Ω resistor in series with a pair of parallel resistors. The parallel resistors are 15 Ω and 30 Ω. Calculate the total resistance of the entire circuit.4 marks
  9. A thermistor is used in a potential divider circuit to act as a temperature sensor. The thermistor has a high resistance when cold and a low resistance when hot. If the output voltage is taken across the thermistor, describe how the output voltage changes as the surroundings get warmer.3 marks
  10. A diode is connected in series with a 100 Ω resistor and a 6 V a.c. supply. Describe the flow of current in the resistor.2 marks

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