An ideal operational amplifier (op-amp) has infinite open-loop gain and infinite input resistance (impedance).

Question 1

(a) An ideal operational amplifier (op-amp) has infinite open-loop gain and infinite input resistance (impedance).

State three further properties of an ideal op-amp. [3]

(b) The circuit of Fig. 10.1 is used to detect changes in temperature.

Fig. 10.1

The voltmeter has infinite resistance.

The variation with temperature θ of the resistance R of the thermistor is shown in Fig. 10.2.

Fig. 10.2

(i) When the thermistor is at a temperature of 1.0 °C, the voltmeter reads +1.0 V.

Show that, for the thermistor at 1.0 °C, the potential at A is −0.20 V. [4]

(ii) The potential at A remains at −0.20 V.

Determine the voltmeter reading for a thermistor temperature of 15 °C. [2]

(c) The voltmeter reading for a thermistor temperature of 29 °C is 0.35 V.

(i) Assuming a linear change of voltmeter reading with change of temperature over the

(ii) Suggest why your answers in (b)(ii) and (c)(i) are not the same. [1]

Reference: Past Exam Paper – November 2014 Paper 41 & 42 Q10

Solution 1:

(a)

zero output resistance / impedance

infinite bandwidth

infinite slew rate

(b)

(i)

{from graph:} at 1.0 °C, thermistor resistance is 3.7 kΩ

{for inverting amplifier: voltage gain = V_out / V_in = - R_f / R_in}

amplifier gain = –R / 740 = –3700 / 740 (negative sign essential)

gain = –5.0      C1

{potential at A = V_in = V_out / gain = = 1.0 / –5.0}

potential at A = 1.0 / –5.0 = –0.20 V  

(ii)

{from graph:} at 15 °C, R = 2.15 kΩ               (allow ±0.05 kΩ)

{V_out = - (R_f / R_in)  V_in}

reading = (2150 / 740) × 0.2

reading = 0.58 V (0.59 V → 0.57 V)  

(c)

(i)

{Since they are assumed to vary linearly, the voltmeter reading is inversely proportional to the temperature (the graph is a straight line with negative gradient).

29 °C corresponds to 0.35 V

1 °C corresponds to 0.35 × 29

15 °C corresponds to 0.35 × 29 / 15 = 0.68 V}

0.68 V

(ii) The resistance (of the thermistor) does not change linearly with temperature