Cambridge Lower Secondary CheckpointStage 9

Physics: Electricity and magnetism

Science Stage 9 Chapter Notes

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Physics: Electricity and magnetism
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In this chapter

  1. 1Introduction to Parallel Circuits
  2. 2Current and Voltage in Parallel
  3. 3Calculating Parallel Resistance
  4. 4Practical Circuits: LDRs and Thermistors

1. Introduction to Parallel Circuits

A parallel circuit provides more than one path for the electric current to flow. Imagine a river splitting into several smaller streams and then joining back together; this is how current behaves in a parallel circuit. Each separate path is called a 'branch'. The key feature is that components on different branches function independently. If a bulb in one branch breaks, the bulbs in the other branches will stay lit because the circuit is not broken for them.

Key term

Parallel Circuit: A closed circuit in which the current divides into two or more paths before recombining to complete the circuit.

Common pitfall

Confusing a parallel circuit diagram with a series circuit. Remember, parallel has junctions where the current splits, while series is a single, unbroken loop.

Fun fact

The electrical wiring in your home is a giant parallel circuit. This is why you can turn on a light in one room without having to turn on every other appliance in the house!

Worked example 13 marks

Draw a circuit diagram for a circuit containing a battery, a switch, and two lamps connected in parallel with each other.

  1. 1

    Step 1: Draw the symbol for a battery (a long line and a shorter, thicker line). Label the positive (+) and negative (-) terminals.

  2. 2

    Step 2: Draw a continuous wire from the positive terminal of the battery to a point where the circuit will split. This point is called a junction.

  3. 3

    Step 3: From the junction, draw two separate branches. On each branch, draw the symbol for a lamp (a circle with a cross inside).

  4. 4

    Step 4: Draw wires to connect the other side of each lamp to a second junction where the branches rejoin.

  5. 5

    Step 5: Draw a wire from the second junction containing the symbol for a switch (a break in the line with a hinged section) back to the negative terminal of the battery to complete the circuit.

Recap

  • A parallel circuit has multiple paths for the current to flow.
  • Components in parallel are connected across the same two points in the circuit.
  • Each branch of a parallel circuit can be switched on or off independently.
  • If one branch of a parallel circuit is broken, the other branches can still operate.
  • Household lighting and wall sockets are wired in parallel.

Quick check

  1. What is the main advantage of connecting household lamps in parallel instead of in series?1 mark
  2. In a parallel circuit, what is a point where the current splits or rejoins called?1 mark

2. Current and Voltage in Parallel

In a parallel circuit, the rules for current and voltage are different from a series circuit. The voltage across each component connected in parallel is the same. If a 12V battery is connected to three resistors in parallel, the potential difference across each resistor will be 12V. The total current flowing from the source, however, is shared between the branches. The total current (I_total) is equal to the sum of the currents in the individual branches (I_total = I1 + I2 + ...). The current splits at a junction and recombines when the branches meet again.

V_supply = V_1 = V_2 = ...

I_total = I_1 + I_2 + ...

Key term

Junction: A point in a circuit where three or more conductors meet, allowing the current to split or recombine.

Examiner insight

Examiners look for a clear understanding that voltage is constant across parallel branches, while current is divided. Stating these two rules explicitly often gains marks in explanation questions.

Fun fact

An ammeter, which measures current, must be placed in series with a component, but a voltmeter, which measures potential difference, must be placed in parallel with it.

Worked example 13 marks

A 9V battery is connected to a parallel circuit with two branches. The current in the first branch is 0.5A. The current in the second branch is 0.3A. What is the total current leaving the battery, and what is the potential difference across the second branch?

  1. 1

    Step 1: Identify the rule for current in a parallel circuit: The total current is the sum of the currents in the branches. I_total = I1 + I2.

  2. 2

    Step 2: Substitute the known values: I_total = 0.5A + 0.3A.

  3. 3

    Step 3: Calculate the total current: I_total = 0.8A.

  4. 4

    Step 4: Identify the rule for voltage in a parallel circuit: The voltage is the same across all branches and equal to the supply voltage.

  5. 5

    Step 5: State the potential difference across the second branch: V2 = V_supply = 9V.

Recap

  • The potential difference (voltage) is the same across all branches in a parallel circuit.
  • The total current from the supply is the sum of the currents in the separate branches.
  • Current splits at junctions and recombines later in the circuit.
  • Each branch may have a different current, depending on its resistance.

Quick check

  1. If the total current entering a junction is 2.0A and it splits into two branches, with 1.2A flowing through the first branch, what is the current in the second branch?1 mark
  2. A 6V battery is connected to three lamps in parallel. What is the voltage across the third lamp?1 mark

3. Calculating Parallel Resistance

The total or 'equivalent' resistance of a parallel circuit is calculated differently from a series circuit. Adding more resistors in parallel always decreases the total resistance of the circuit. This is because adding another branch provides an extra path for the current to flow, making it easier for charge to move through the circuit overall. The formula involves adding the reciprocals of the individual resistances. A key consequence is that the total resistance in a parallel circuit is always less than the smallest individual resistance in any of the branches.

1/R_total = 1/R_1 + 1/R_2 + 1/R_3 + ...

For two resistors: R_total = (R_1 * R_2) / (R_1 + R_2)

Key term

Equivalent Resistance: The total effective resistance of a combination of resistors in a circuit; a single resistor that would have the same effect as the combination.

Examiner insight

Examiners often set multi-step problems where you must first calculate the total resistance of a parallel section before using Ohm's Law to find a current or voltage.

Common pitfall

A very common mistake is calculating 1/R_total and forgetting to perform the final step of inverting the result to find R_total. For example, giving the answer as 0.5 instead of 2Ω.

Worked example 13 marks

Two resistors, one of 6Ω and one of 3Ω, are connected in parallel. Calculate their total equivalent resistance.

  1. 1

    Step 1: Write down the formula for total resistance in parallel: 1/R_total = 1/R1 + 1/R2.

  2. 2

    Step 2: Substitute the given values: 1/R_total = 1/6 + 1/3.

  3. 3

    Step 3: Find a common denominator to add the fractions: 1/R_total = 1/6 + 2/6.

  4. 4

    Step 4: Add the fractions: 1/R_total = 3/6 = 1/2.

  5. 5

    Step 5: This gives the value of 1/R_total. To find R_total, take the reciprocal (invert the fraction): R_total = 2/1 = 2Ω.

Worked example 24 marks

A 12V power supply is connected to two resistors in parallel: a 10Ω resistor and a 15Ω resistor. Calculate the total current flowing from the supply.

  1. 1

    Step 1: First, calculate the total resistance of the parallel combination. 1/R_total = 1/R1 + 1/R2.

  2. 2

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

  3. 3

    Step 3: Find a common denominator (30): 1/R_total = 3/30 + 2/30 = 5/30.

  4. 4

    Step 4: Simplify and find R_total by taking the reciprocal: 1/R_total = 1/6, so R_total = 6Ω.

  5. 5

    Step 5: Use Ohm's Law (V = IR) to find the total current. Rearrange for I: I_total = V_total / R_total.

  6. 6

    Step 6: Substitute values and calculate: I_total = 12V / 6Ω = 2A.

Recap

  • Adding a resistor in parallel decreases the total resistance.
  • The total resistance of a parallel circuit is always less than the smallest individual resistor.
  • The formula for total resistance is 1/R_total = 1/R1 + 1/R2 + ...
  • Always remember to take the final reciprocal to find R_total, not 1/R_total.

Quick check

  1. If you connect a 100Ω resistor in parallel with a 1Ω resistor, will the total resistance be closer to 100Ω or 1Ω?1 mark

4. Practical Circuits: LDRs and Thermistors

Practical circuits often use components whose resistance changes in response to the environment. Two key examples are Light Dependent Resistors (LDRs) and Thermistors. The resistance of an LDR is very high in the dark but decreases as light intensity increases. The resistance of a standard (NTC) thermistor is high at low temperatures but decreases as it gets hotter. These components are often used in a 'potential divider' circuit, where the supply voltage is shared between the special resistor and a fixed resistor. As the resistance of the LDR or thermistor changes, the voltage across it also changes, allowing the circuit to sense changes in light or temperature.

V_out = V_in * (R_2 / (R_1 + R_2))

Key term

Potential Divider: A simple circuit that uses two or more resistors (or a variable resistor) to produce a specific output voltage that is a fraction of the source voltage.

Examiner insight

For questions on sensing circuits, examiners reward a logical chain of reasoning: physical change -> resistance change -> voltage/current change -> circuit action.

Fun fact

The sensor in your phone's screen that automatically adjusts the brightness is based on an LDR or a similar photodiode, constantly measuring ambient light.

Worked example 14 marks

A circuit for an automatic night light uses a 12V supply, an LDR and a 1000Ω fixed resistor in series. The LDR is placed in series with the fixed resistor. Explain what happens to the potential difference across the fixed resistor as it gets dark.

  1. 1

    Step 1: State the behaviour of the LDR. As it gets dark, the light intensity decreases.

  2. 2

    Step 2: Link light intensity to the LDR's resistance. A decrease in light intensity causes the resistance of the LDR to increase significantly.

  3. 3

    Step 3: Consider the potential divider circuit. The total resistance of the circuit (R_LDR + R_fixed) increases.

  4. 4

    Step 4: Relate the change in resistance to the share of voltage. Since the LDR's resistance has increased, it will take a larger share of the supply voltage.

  5. 5

    Step 5: Conclude the effect on the fixed resistor. As the LDR takes a larger share of the voltage, the fixed resistor must take a smaller share. Therefore, the potential difference across the fixed resistor decreases.

Recap

  • An LDR's resistance decreases as light intensity increases.
  • A thermistor's resistance decreases as temperature increases (for NTC type).
  • These components are used in potential divider circuits to create sensors.
  • In a potential divider, the voltage is shared between components in proportion to their resistance.
  • A change in light or temperature causes a change in resistance, which in turn causes a change in the output voltage.

Quick check

  1. For a fire alarm circuit, would you use an LDR or a thermistor?1 mark
  2. A thermistor is used in a thermostat. As the room cools down, what happens to the thermistor's resistance?1 mark

End-of-chapter exercise

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

  1. A 10Ω resistor and a 20Ω resistor are connected in parallel to a 6V battery. Calculate (a) the total resistance of the circuit, and (b) the total current flowing from the battery.4 marks
  2. Draw a circuit diagram to show a cell connected to two bulbs in parallel. Include a switch that controls both bulbs, and another switch that controls only one of the bulbs.4 marks
  3. Explain why connecting more lamps in parallel to a mains supply decreases the total resistance of the circuit, and what effect this has on the total current drawn from the supply.3 marks
  4. A circuit contains three resistors in parallel: R1 = 5Ω, R2 = 10Ω, and R3 = 10Ω. The total current flowing into the parallel combination is 4A. Calculate the potential difference across the combination.4 marks
  5. A potential divider consists of a thermistor and a 2kΩ fixed resistor connected in series to a 10V supply. At room temperature, the thermistor has a resistance of 3kΩ. Calculate the potential difference across the fixed resistor at this temperature.3 marks
  6. Describe the difference in how current and voltage behave in a series circuit compared to a parallel circuit.4 marks
  7. A student has two identical resistors. The total resistance is R_S when they are connected in series, and R_P when they are connected in parallel. If R_S = 80Ω, what is the value of R_P?4 marks
  8. A sensing circuit is designed to switch on a fan when a room gets too hot. It uses a thermistor. Should the fan be triggered by a high or a low voltage across the thermistor? Explain your reasoning.3 marks
  9. Three resistors are connected in parallel to a 12V supply. The currents in the branches are 0.6A, 0.4A, and 0.2A. Calculate (a) the resistance of each resistor, and (b) the total power dissipated by the circuit.5 marks
  10. Explain why adding an extra resistor in parallel with other resistors always decreases the total resistance.2 marks

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