Friday, March 31, 2017

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 = Vout / Vin = - Rf / Rin}
amplifier gain = –R / 740 = –3700 / 740 (negative sign essential)
gain = –5.0      C1
{potential at A = Vin = Vout / 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)
{Vout = - (Rf / Rin)  Vin}
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

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