AQA A-Level Physics: Difference Amplifier Configuration and Output Voltage Calculation — mark scheme explained

The question

Calculate the output voltage of a summing amplifier if V 1 = 4V, R 1 = 2kΩ, V 2 = 6V, and R 2 = 3kΩ. [Paraphrased for study — not reproduced from any exam paper.]

Mark scheme, decoded

What each mark is really for — in plain English — and the wording trap that loses it.

• S1

  Step 1: Identify the given values. - V 1 = 4V - R 1 = 2kΩ - V 2 = 6V - R 2 = 3kΩ - Feedback resistor R f = 1kΩ (the question omits R f ; we take the standard assumed value R f = 1kΩ).

• S2

  Step 2: Use the summing amplifier formula. V out = - R f × (V 1 /R 1 + V 2 /R 2 )

• S3

  Step 3: Calculate each input current. - V 1 /R 1 = 4V/2kΩ = 2mA - V 2 /R 2 = 6V/3kΩ = 2mA

• S4

  Step 4: Sum the input currents. V 1 /R 1 + V 2 /R 2 = 2mA + 2mA = 4mA

• S5

  Step 5: Multiply by -R f . V out = - 1kΩ × 4mA = - (1 × 10 3 Ω) × (4 × 10 -3 A) = -4 V

Model answer

Worked through, with each step tagged to the mark it earns.

1. S1

   Step 1: Identify the given values. - V 1 = 4V - R 1 = 2kΩ - V 2 = 6V - R 2 = 3kΩ - Feedback resistor R f = 1kΩ (the question omits R f ; we take the standard assumed value R f = 1kΩ).

2. S2

   Step 2: Use the summing amplifier formula. V out = - R f × (V 1 /R 1 + V 2 /R 2 )

3. S3

   Step 3: Calculate each input current. - V 1 /R 1 = 4V/2kΩ = 2mA - V 2 /R 2 = 6V/3kΩ = 2mA

4. S4

   Step 4: Sum the input currents. V 1 /R 1 + V 2 /R 2 = 2mA + 2mA = 4mA

5. S5

   Step 5: Multiply by -R f . V out = - 1kΩ × 4mA = - (1 × 10 3 Ω) × (4 × 10 -3 A) = -4 V

6. Final answer: Vout = -4 V (assuming Rf = 1 kΩ — question is missing Rf)

Common mistakes

• Forgetting the negative sign in the summing amplifier formula. — Always include the negative sign when using the summing amplifier formula.
• Using inconsistent units for voltages and resistances. — Ensure all values are in consistent units before performing calculations.
• Confusing the roles of R f and R 1 in the difference amplifier formula. — Clearly identify R f as the feedback resistance and R 1 as the input resistance.
• Forgetting to calculate the difference between V 2 and V 1 in the difference amplifier formula. — Always subtract V 1 from V 2 when using the difference amplifier formula.
• Not matching input resistances in a difference amplifier for accurate measurements. — Ensure that the input resistances are matched to avoid measurement errors.
• Using the wrong formula for a given configuration (summing vs. difference amplifier). — Clearly identify whether the circuit is a summing or difference amplifier and use the appropriate formula.

Where the marks go

• Full worked solution (all marking points)4 marks

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