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Cambridge International AS & A Level · 10 · structured

Reduce a network and design sensor outputs

Reduce a network and design sensor outputs · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
17
Topics
4
Answer
Complete
structured17 marks

Circuit A: an ideal12.0 V source feeds a3.0Ω series resistor followed by 6.0Ω and12.0Ω in parallel. Circuit B: an ideal6.0 V source has a fixed2.0kΩ upper resistor from+6 V to output node X and a sensor from X to 0 V; output is V_X relative to 0 V and is unloaded.

  1. (a)

    For circuit A, find the parallel equivalent, complete circuit resistance, total current and each parallel branch current. Show the common p.d. used.

    5 marks
  2. (b)

    Derive V_X=6.0R_sensor/(2.0kΩ+R_sensor) from the common current. Find output when R_sensor=4.0kΩ and explain the unloaded assumption.

    4 marks
  3. (c)

    If the lower sensor is an LDR changing from 8.0kΩ in darkness to 1.0kΩ in bright light, calculate both outputs and predict the trend. Replace it with an NTC thermistor: predict output on warming. Explain how swapping sensor and fixed-resistor positions reverses each trend.

    5 marks
  4. (d)

    State Kirchhoff's first law and the conservation principle it expresses. At a junction, currents2.0 A and1.5 A enter while0.8 A leaves in one branch. Determine the remaining branch current and direction for a steady circuit.

    3 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overview(a) ParallelR=4.0Ω; total7.0Ω; totalI=12/7=1.71 A; parallelV=48/7=6.86 V;6Ω branch8/7=1.14 A,12Ω branch4/7=0.571 A. (b) I=6.0/(R_fixed+R_sensor); V_X=IR_sensor=4.0 V for4kΩ. Unloaded means negligible output current, so the two resistor currents remain equal. (c) LDR output falls from 4.8 V to 2.0 V as light rises. NTC warming also lowers sensorR and output. With sensor on top and output across fixed lower resistor, reduced sensorR increases output. (d) Sum of entering currents equals sum leaving, expressing charge conservation/no steady charge buildup. Remaining3.5−0.8=2.7 A leaves the junction.
01

(a)

5 marks

For circuit A, find the parallel equivalent, complete circuit resistance, total current and each parallel branch current. Show the common p.d. used.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    Use 1/Rp=1/6+1/12=1/4.

  2. 2

    Add series3Ω for7Ω.

  3. 3

    Find source current12/7 A.

  4. 4

    Find parallel p.d.I×4=48/7 V.

  5. 5

    Divide common p.d. by each branchR and check branch sum.

02

(b)

4 marks

Derive V_X=6.0R_sensor/(2.0kΩ+R_sensor) from the common current. Find output when R_sensor=4.0kΩ and explain the unloaded assumption.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    Use series totalR and commonI.

  2. 2

    Output is specifically across the lower sensor.

  3. 3

    Substitute ratio4/(2+4) for4 V.

  4. 4

    State no appreciable load current alters the divider.

03

(c)

5 marks

If the lower sensor is an LDR changing from 8.0kΩ in darkness to 1.0kΩ in bright light, calculate both outputs and predict the trend. Replace it with an NTC thermistor: predict output on warming. Explain how swapping sensor and fixed-resistor positions reverses each trend.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    Evaluate6×8/(2+8)=4.8 V and6×1/(2+1)=2.0 V.

  2. 2

    State the output spans the lower element, so its falling resistance reduces its share.

  3. 3

    Apply same reasoning to NTC warming.

  4. 4

    After swapping positions, output=6R_fixed/(R_sensor+R_fixed), rising as sensorR falls.

04

(d)

3 marks

State Kirchhoff's first law and the conservation principle it expresses. At a junction, currents2.0 A and1.5 A enter while0.8 A leaves in one branch. Determine the remaining branch current and direction for a steady circuit.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    State correct current-sum law.

  2. 2

    Name conservation of charge and no steady accumulation.

  3. 3

    Calculate and label2.7 A outward.

Complete marking guidance

Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.

  1. (a) Use 1/Rp=1/6+1/12=1/4.
  2. (a) Add series3Ω for7Ω.
  3. (a) Find source current12/7 A.
  4. (a) Find parallel p.d.I×4=48/7 V.
  5. (a) Divide common p.d. by each branchR and check branch sum.
  6. (b) Use series totalR and commonI.
  7. (b) Output is specifically across the lower sensor.
  8. (b) Substitute ratio4/(2+4) for4 V.
  9. (b) State no appreciable load current alters the divider.
  10. (c) Evaluate6×8/(2+8)=4.8 V and6×1/(2+1)=2.0 V.
  11. (c) State the output spans the lower element, so its falling resistance reduces its share.
  12. (c) Apply same reasoning to NTC warming.
  13. (c) After swapping positions, output=6R_fixed/(R_sensor+R_fixed), rising as sensorR falls.
  14. (d) State correct current-sum law.
  15. (d) Name conservation of charge and no steady accumulation.
  16. (d) Calculate and label2.7 A outward.

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