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physics A-Level Physics
 
Solved problems for the chapter:
 

Op-Amp, Inverting and Non-Inverting Amplifiers

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Example 1.

In a strain gauge, the increase in resistance depends on the increase in length . The variation of with is shown in the graph below.




The strain gauge is connected into a circuit incorporating an ideal operational amplifier (op-amp), as shown in the figure below.




  • The strain gauge is initially unstrained with resistance . Use data from the graph above to calculate the increase in length of the strain gauge that gives rise to a potential of at point A in the figure above.


  • The strain gauge undergoes a further increase in length beyond the value in (a). State and explain which one of the light-emitting diodes, X or Y, will be emitting light.

    
Example 2.

  • By reference to an amplifier, explain what is meant by negative feedback.


  • An amplifier circuit incorporating an ideal operational amplifier (op-amp) is shown in the figure below.




    The supply for the op-amp is . The amplifier circuit is to have a gain of 25. Calculate the resistance of resistor R.


  • State the value of the output voltage of the amplifier in (b) for input voltages of





    
3.

The circuit diagram in the figure below is an amplifier circuit incorporating an operational amplifier (op-amp).




  • On the figure above, mark, with the letter X, the virtual earth.


  • In bright sunlight, the light-dependent resistor (LDR) has resistance .


    • Calculate, for the LDR in bright sunlight, the voltmeter reading.


    • The sunlight incident on the LDR becomes less bright. State and explain the effect on the voltmeter reading of this decrease in brightness.

    
4.

  • State two effects of negative feedback on the gain of an amplifier incorporating an operational amplifier (op-amp).


  • An incomplete diagram of an amplifier circuit incorporating an ideal operational amplifier is shown in the figure below.




    The amplifier has a voltage gain of .


    • Complete the circuit diagram in the figure above.


    • Calculate the resistance of any additional resistor you have drawn on the figure above.

    
5.

  • An operational amplifier (op-amp) may be used as a comparator. State the function of a comparator.


  • The variation with temperature of the resistance of a thermistor is shown in the graph below.




    The thermistor is connected into the circuit shown in the figure below.




    The op-amp may be considered to be ideal.


    • The temperature of the thermistor is . Determine the resistance of the variable resistor X such that the output potential is zero.


    • The resistance of the resistor X is now held constant at the value calculated in (i). Describe the change in the output potential as the temperature of the thermistor is changed from to .

    
6.

  • Two properties of an ideal operational amplifier (op-amp) are infinite input impedance and infinite bandwidth. State what is meant by:


    • infinite input impedance


    • infinite bandwidth.


  • A student uses a negative temperature coefficient thermistor in the circuit shown in the figure below to indicate changes in temperature.




    • Show that the potential at point X is .


    • The thermistor has a resistance of at a particular temperature. For this temperature of the thermistor, calculate the magnitude of the reading on the voltmeter.


    • The temperature of the thermistor increases. State and explain the effect of this change on the magnitude of the reading on the voltmeter.


    • Explain why the amplifier circuit will no longer indicate temperature changes when the magnitude of the gain of the circuit is greater than .

    
7.

A strain gauge S is connected into the circuit shown in the figure below.




The operational amplifier (op-amp) is ideal. The output potential of the circuit is given by the expression




  • State the name given to the ratio .


  • The strain gauge S has resistance when not under strain. Calculate the magnitude of such that, when the strain gauge S is not strained, the output is zero.


  • In a particular test, the resistance of S increases to . is unchanged. The ratio is 12. Calculate the magnitude of .

    
8.

The variation with temperature of the resistance of a thermistor is shown in the graph below.




A student includes the thermistor and an ideal operational amplifier (op-amp) in the circuit shown in the figure below.




  • Calculate the potential at the non-inverting input of the op-amp.


  • At , the resistance of the thermistor is . State and explain whether the light-emitting diode (LED) is emitting light.


  • Explain why the student’s circuit will not indicate any change in temperature above .


  • The resistor of resistance is changed to a resistor of resistance so that the LED switches on or off at a temperature of . Determine in .

    

9.

An operational amplifier (op-amp) may be used as part of the processing unit in an electronic sensor. State four properties of an ideal operational amplifier.

    
10.

  • An ideal operational amplifier (op-amp) is connected to a load resistor. The op-amp is assumed to have infinite bandwidth and zero output resistance. State:


    • what is meant by infinite bandwidth


    • the effect, if any, on the output voltage of increasing the load resistance.


  • A student designs the circuit shown in the figure below in order to indicate changes in the temperature of the thermistor T.




    • Calculate the potential at point Q.


    • At a temperature of , the resistance of the thermistor T is . Show that the potential difference measured with the voltmeter is .


  • The resistance of the thermistor T in (b) decreases as its temperature rises. Explain the effect of this change in temperature on the potential difference measured with the voltmeter.

    
11.

  • Negative feedback may be used in amplifier circuits. State


    • what is meant by negative feedback,


    • two effects of negative feedback on an amplifier incorporating an operational amplifier (op-amp).


  • The figure below is a circuit for an amplifier that is used with a microphone.




    The output potential difference is when the potential at point P is . Determine


    • the gain of the amplifier,


    • the resistance of the resistor R.


  • The maximum potential produced by the microphone at point P on the figure above is . The power supply for the operational amplifier may be either or . State which power supply should be used. Justify your answer quantitatively.

    
12.

The output of a microphone is processed using a non-inverting amplifier. The amplifier incorporates an operational amplifier (op-amp).


  • State, by reference to the input and output signals, the function of a non-inverting amplifier.


  • The circuit for the microphone and amplifier is shown in the figure below.




    The output potential difference is when the potential at point P is . Determine


    • the gain of the amplifier circuit


    • the resistance of resistor R.


  • For the circuit in the figure above:


    • suggest a suitable device to connect to the output such that the shape of the waveform of the sound received by the microphone may be examined.


    • state and explain the effect on the output potential difference of increasing the resistance of resistor R.

    
13.

  • A circuit incorporating an ideal operational amplifier (op-amp) is shown in the figure below.




    • State the name of this circuit.


    • Explain why the point P is referred to as a virtual earth.


  • The circuit in the figure above is modified, as shown in the figure below.




    The voltmeter has infinite resistance and its full-scale deflection is . The input potential to the circuit is . The switch position may be changed in order to have different values of resistance in the circuit. The input potential and the switch position are varied. For each switch position, the reading of the voltmeter is . Complete the table below for the switch positions shown.



    
14.

The circuit for an inverting amplifier incorporating an ideal operational amplifier (op-amp) is shown in the figure below.




  • calculate the gain of the amplifier.


  • When the op-amp is saturated, the potential difference across the LED is . Calculate the minimum resistance of resistor R so that the current in the LED is limited to .

    
15.

An operational amplifier (op-amp) is used in the comparator circuit shown in the figure below.




  • Show that the potential at the inverting input of the op-amp is .


  • Explain why the potential difference across resistor R is when is greater than and is zero when is less than .

    
16.

  • Negative feedback is often used in amplifiers incorporating an operational amplifier (op-amp). State


    • what is meant by negative feedback,


    • two effects of negative feedback on the gain of an amplifier.


  • An ideal op-amp is incorporated into the amplifier circuit shown in the figure below.




    • Calculate the gain G of the amplifier circuit.


    • Determine the output potential difference for input potential differences of





    
17.

An inverting amplifier, incorporating an operational amplifier (op-amp), uses a high-resistance voltmeter to display the output. A partially completed circuit for the amplifier is shown in the figure below.




The voltmeter is to indicate a full-scale deflection of for an input potential of .


  • On the figure above,


    • complete the circuit for the inverting amplifier,


    • mark, with the letter P, the positive terminal of the voltmeter.


  • Suggest appropriate values for the resistors you have shown in the figure. Label the resistors in the figure with these values.

    
18.

A student designs a circuit incorporating an operational amplifier (op-amp) as shown in the figure below.




  • State the purpose of this circuit.


  • The resistors X and Y each have resistance . When conducting, the LED labelled B emits blue light and the LED labelled G emits green light.


    • State whether blue light or green light is emitted when the resistance of component C is greater than the resistance of the variable resistor. Explain your answer.


    • State and explain what is observed as the resistance of component C is reduced.

    

19.

The circuit of an inverting amplifier incorporating an ideal operational amplifier (op-amp) is shown in the figure below.




  • Explain why point P is known as a virtual earth.


  • Derive an expression, in terms of the resistances and , for the gain of the amplifier circuit. Explain your working.

    
20.

An ideal operational amplifier (op-amp) has infinite voltage gain and infinite slew rate.


  • State what is meant by


    • the voltage gain,


    • infinite slew rate.



  • A non-inverting amplifier circuit incorporating an ideal op-amp is shown in the figure below.




    The supply to the op-amp is / . The voltage gain of the amplifier circuit is 12. Determine the resistance of resistor R.