For

1
Examiner’s
Use

a
aky
1 (a) State three characteristics of an ideal operational amplifier (op-amp).

1. .....................................................................................................................................

Sh
2. .....................................................................................................................................

dra
3. ................................................................................................................................ [3]

(b) An amplifier circuit for a microphone is shown in Fig. 8.1.

an
–

Ch
+

jit
Sa 120 kΩ

R
V OUT
by

X
ed

Fig. 8.1
ng

(i) Name the type of feedback used with this op-amp.

rra

............................................................................................................................. [1]
ea

(ii) The output potential difference VOUT is 5.8 V for a potential difference across the
resistor R of 69 mV. Calculate
dr

1. the gain of the amplifier circuit,

d an
ile
mp
Co

gain = ……………………… [1]

© UCLES 2007 9702/04/M/J/07

 For
2
Examiner’s
Use
2. the resistance of resistor X.

a
aky
Sh
ra
nd
resistance = ……………………… Ω [2]

ha
(iii) State one effect on the amplifier output of reducing the resistance of resistor X.

..................................................................................................................................

tC
............................................................................................................................. [1]
aji
yS
e db
ng
rra
rea
nd
da
ile
mp
Co

© UCLES 2007 9702/04/M/J/07

 3

For
Examiner’s
Use

a
2 A block diagram for an electronic sensor is shown in Fig. 9.1.

aky
output

Sh
device

ra
Fig. 9.1

nd
(a) Complete Fig. 9.1 by labelling the remaining boxes. [2]

ha
(b) A device is to be built that will emit a red light when its input is at +2 V. When the input is
at –2 V, the light emitted is to be green.

tC
(i) On Fig. 9.2, draw a circuit diagram of the device.

input
aji
yS
either + 2V
or – 2V
e db
ng
rra
rea

[2]
Fig. 9.2
nd

(ii) Explain briefly the action of this device.

da

..................................................................................................................................

.............................................................................................................................. [1]
ile
mp
Co

© UCLES 2008 9702/04/M/J/08

 4

For
Examiner’s
Use

a
aky
3 (a) By reference to an amplifier, explain what is meant by negative feedback.

..........................................................................................................................................

Sh
..........................................................................................................................................

ra
.................................................................................................................................... [2]

nd
(b) An amplifier circuit incorporating an ideal operational amplifier (op-amp) is shown in
Fig. 10.1.

ha
–

tC
+

V IN 120 kΩ
aji V OUT
yS
R
e db

Fig. 10.1
ng

The supply for the op-amp is ± 9.0 V.

The amplifier circuit is to have a gain of 25.
rra

Calculate the resistance of resistor R.

rea
nd
da
ile

resistance = ........................................... Ω [2]

mp

(c) State the value of the output voltage VOUT of the amplifier in (b) for input voltages VIN of

(i) – 0.08 V,
Co

VOUT = ............................................ V [1]

(ii) +0.4 V.

VOUT = ............................................ V [1]

© UCLES 2009 9702/04/M/J/09
 For
5
Examiner’s
Use

a
aky
4 (a) Fig. 8.1 shows a circuit incorporating an ideal operational amplifier (op-amp).

+ 9V

Sh
–

ra
+

nd
– 9V
V1

ha
VOUT
V2

tC
aji
yS
Fig. 8.1

The voltages applied to the inverting and the non-inverting inputs are V1 and V2
db

respectively.

State the value of the output voltage VOUT when

e
ng

(i) V1 > V2,

VOUT = .................................................... V
rra

(ii) V1 < V2.

rea

VOUT = .................................................... V
[1]
nd
da
ile
mp
Co

© UCLES 2007 9702/04/O/N/07

 For
6
Examiner’s
Use
(b) The circuit of Fig. 8.2 is used to monitor the input voltage VIN.

+V

a
aky
A
+5.0V –

Sh
+

ra
B

nd
+3.0V –
+
VIN

ha
red green

tC
aji
yS
Fig. 8.2

At point A, a potential of 5.0 V is maintained. At point B, a potential of 3.0 V is

db

maintained.
e

Complete Fig. 8.3 by indicating with a tick (✓) the light-emitting diodes (LEDs) that are
conducting for the input voltages VIN shown. Also, mark with a cross ( ) those LEDs that
ng

are not conducting.

rra

VIN / V red LED green LED

+2.0
rea

+4.0

+6.0
nd

[3]
da

Fig. 8.3
ile
mp
Co

© UCLES 2007 9702/04/O/N/07

 For
7
Examiner’s
Use
(c) The input voltage VIN in (b) is provided by a sensor circuit.

(i) Complete Fig. 8.4 to show a sensor circuit that will provide a voltage output that
increases as the temperature of the sensor decreases. Show clearly the output

a
connections from the circuit. [2]

aky
Sh
ra
nd
ha
tC
(ii) Explain the operation of the sensor circuit.
Fig. 8.4
aji
yS
..................................................................................................................................
db

..................................................................................................................................

..................................................................................................................................
e
ng

..................................................................................................................................
rra

..................................................................................................................................

..............................................................................................................................[3]
rea
nd
da
ile
mp
Co

© UCLES 2007 9702/04/O/N/07

 8

5 (a) The circuit for an amplifier incorporating an ideal operational amplifier (op-amp) is shown For
in Fig. 10.1. Examiner’s
Use

a
R2

aky
R1 +9 V
–
P

Sh
+
VIN –9 V VOUT

ra
nd
ha
Fig. 10.1

tC
(i) State

1. the name of this type of amplifier circuit, aji

.............................................................................................................................. [1]
yS
2. why the point P is referred to as a virtual earth.
db

..................................................................................................................................
e

..................................................................................................................................
ng

..................................................................................................................................
rra

.............................................................................................................................. [3]

(ii) Show that the gain G of this amplifier circuit is given by the expression
rea

R2
G = – ––– .
R1
Explain your working.
nd
da
ile
mp
Co

[4]

© UCLES 2008 9702/04/O/N/08

 9

(b) The circuit of Fig. 10.1 is modified by connecting a light-dependent resistor (LDR) as For
shown in Fig. 10.2. Examiner’s
Use

a
aky
R2

Sh
R1 +9 V
–

ra
+

nd
VIN = +1.2 V –9 V VOUT
V

ha
tC
Fig. 10.2
aji
The resistances R1 and R2 are 5.0 kΩ and 50 kΩ respectively.
yS
The input voltage VIN is +1.2 V. A high-resistance voltmeter measures the output VOUT.
The circuit is used to monitor low light intensities.
db

(i) Determine the voltmeter reading for light intensities such that the LDR has a
resistance of
e

1. 100 kΩ,
ng
rra
rea
nd

reading = .............................................. V [3]

da

2. 10 kΩ.
ile
mp
Co

reading = .............................................. V [2]

© UCLES 2008 9702/04/O/N/08
 10

(ii) The light incident on the LDR is provided by a single lamp. Use your answers in (i) For
to describe and explain qualitatively the variation of the voltmeter reading as the Examiner’s
lamp is moved away from the LDR. Use

a
..................................................................................................................................

aky
..................................................................................................................................

..................................................................................................................................

Sh
..................................................................................................................................

ra
.............................................................................................................................. [3]

nd
ha
tC
aji
yS
e db
ng
rra
rea
nd
da
ile
mp
Co

© UCLES 2008 9702/04/O/N/08

 11

For
Examiner’s
Use

a
aky
6 A metal wire strain gauge is firmly fixed across a crack in a wall, as shown in Fig. 9.1, so that
the growth of the crack may be monitored.

Sh
strain crack
gauge

dra
an
Ch
jit
Fig. 9.1 Sa
(a) Explain why, as the crack becomes wider, the resistance of the strain gauge increases.

..........................................................................................................................................
by

..........................................................................................................................................
ed

..........................................................................................................................................
ng

.................................................................................................................................... [3]

(b) The strain gauge has an initial resistance of 143.0 Ω and, after being fixed in position
rra

across the crack for several weeks, the resistance is found to be 146.2 Ω.

The change in the area of cross-section of the strain gauge wire is negligible.
ea

Calculate the percentage increase in the width of the crack. Explain your working.
dr
d an
ile
mp

increase = ........................................... % [3]

Co

© UCLES 2009 9702/41/O/N/09

 12

7 The circuit of Fig. 10.1 may be used to indicate temperature change. For
Examiner’s
Use
+2 V

a
aky
T P
+5V

Sh
+

–5V

dra
P P R G

an
Ch
Fig. 10.1

The resistance of the thermistor T at 16 °C is 2100 Ω and at 18 °C, the resistance is 1900 Ω.

jit
Each resistor P has a resistance of 2000 Ω. Sa
Determine the change in the states of the light-emitting diodes R and G as the temperature
of the thermistor changes from 16 °C to 18 °C.
by
ed
ng
rra
ea

.................................................................................................................................................

........................................................................................................................................... [4]
dr
d an
ile
mp
Co

© UCLES 2009 9702/41/O/N/09

 13

For
Examiner’s
Use

a
aky
8 An amplifier incorporating an operational amplifier (op-amp) has three inputs A, B and C, as
shown in Fig. 9.1.

Sh
8.0 kΩ

A 2.0 kΩ RF

dra
+9 V
B 4.0 kΩ
–

an
C 8.0 kΩ +
VA
VB –9 V

Ch
VOUT
VC

jit
Sa
Fig. 9.1
by

Negative feedback is provided by the resistor RF of resistance 8.0 k.

For each of the inputs A, B and C, the amplifier may be considered as a single input amplifier.
ed

That is, each input is independent of the other two.

When the amplifier is not saturated, the output potential VOUT is given by the expression
ng

VOUT = –(4VA + GVB + VC),

rra

where VA, VB and VC are the input potentials of the inputs A, B and C respectively and G is a
constant.
ea

(a) State two effects of negative feedback on an amplifier.

dr

1. ......................................................................................................................................
an

..........................................................................................................................................

2. ......................................................................................................................................
d
ile

..........................................................................................................................................
[2]
mp
Co

© UCLES 2009 9702/42/O/N/09

 14

(b) In the expression for the output potential VOUT , the constant G is the gain associated For
with input B. Show that the numerical value of G is 2. Examiner’s
Use

a
aky
Sh
dra
[1]

an
(c) The input potentials VA, VB and VC are either zero or 1.0 V.

Ch
The magnitudes of some output potentials for different combinations of VA, VB and VC
are shown in Fig. 9.2.

VA / V VB / V jit
VC / V VOUT / V
Sa
0 0 1 1
by

0 1 0 ……
ed

1 0 0 4

1 0 1 5
ng

1 1 0 ……
rra

1 1 1 ……
ea

Fig. 9.2
dr

(i) Complete Fig. 9.2 for the three remaining values of VOUT . [1]
an

(ii) Suggest a use for this circuit.

............................................................................................................................ [1]
d
ile
mp
Co

© UCLES 2009 9702/42/O/N/09

 For
Examiner’s
Use

9 (a) Negative feedback may be used in amplifier circuits. State

(i) what is meant by negative feedback,

..................................................................................................................................

ya
..................................................................................................................................

ak
............................................................................................................................ [2]

Sh
(ii) two effects of negative feedback on an amplifier incorporating an operational

ra
amplifier (op-amp).

d
1. ...............................................................................................................................

an
..................................................................................................................................

Ch
2. ...............................................................................................................................
jit
..................................................................................................................................
[2]
Sa

(b) Fig. 9.1 is a circuit for an amplifier that is used with a microphone.
by

P
ed
ng

microphone 120 kΩ
ra

V OUT
r
ea

R
r
nd
da

Fig. 9.1
ile
mp

The output potential difference VOUT is 4.4 V when the potential at point P is 62 mV.

Determine
Co

(i) the gain of the amplifier,

gain = ............................................... [1]

© UCLES 2010 9702/43/M/J/10
 (ii) the resistance of the resistor R. For
Examiner’s
Use

ya
ak
resistance = .......................................... Ω [2]

Sh
(c) The maximum potential produced by the microphone at point P on Fig. 9.1 is 95 mV.

ra
The power supply for the operational amplifier may be either +/– 5 V or +/– 9 V.

d
State which power supply should be used. Justify your answer quantitatively.

an
..........................................................................................................................................

Ch
..........................................................................................................................................
jit
..........................................................................................................................................
Sa

.................................................................................................................................... [3]
by
ed
ng
r ra
r ea
nd
da
ile
mp
Co

© UCLES 2010 9702/43/M/J/10 [Turn over

10 (a) State the name of an electrical sensing device that will respond to changes in For
Examiner’s
(i) length, Use

............................................................................................................................ [1]

(ii) pressure.

............................................................................................................................ [1]

ya
(b) A relay is sometimes used as the output of a sensing circuit.

ak
The output of a particular sensing circuit is either + 2 V or – 2 V.

Sh
On Fig. 10.1, draw symbols for a relay and any other necessary component so that the

ra
external circuit is switched on only when the output from the sensing circuit is + 2 V.

d
an
Ch
+2 V or –2 V
jit
Sa
output from terminals
of external
by

sensing circuit
circuit
ed
ng
ra

Fig. 10.1
r
ea

[4]
r
nd
da
ile
mp
Co

© UCLES 2010 9702/43/M/J/10

 For
Examiner’s
Use

11 The circuit diagram of Fig. 9.1 is an amplifier circuit incorporating an operational amplifier
(op-amp).

4.2 kΩ

ya
1.0 kΩ +9 V

ak
–
+

Sh
1.5 V +
–9 V V
–

d ra
an
Fig. 9.1

Ch
(a) (i) On Fig. 9.1, mark, with the letter X, the virtual earth. [1]

(ii) Explain what is meant by a virtual earth.

jit
Sa
..................................................................................................................................
by

..................................................................................................................................
ed

..................................................................................................................................
ng

.............................................................................................................................. [3]
ra

(b) In bright sunlight, the light-dependent resistor (LDR) has resistance 200 Ω.
r
ea

(i) Calculate, for the LDR in bright sunlight, the voltmeter reading.
r
nd
da
ile
mp
Co

reading = ............................................ V [3]

© UCLES 2010 9702/41/M/J/10

 (ii) The sunlight incident on the LDR becomes less bright. For
State and explain the effect on the voltmeter reading of this decrease in Examiner’s
brightness. Use

..................................................................................................................................

..................................................................................................................................

..................................................................................................................................

ya
.............................................................................................................................. [3]

ak
Sh
d ra
an
Ch
jit
Sa
by
ed
ng
r ra
r ea
nd
da
ile
mp
Co

© UCLES 2010 9702/41/M/J/10 [Turn over

 18

Section B For
Examiner’s
Answer all the questions in the spaces provided. Use

9 An amplifier circuit incorporating an operational amplifier (op-amp) is shown in Fig. 9.1.

ya
R2

k
ha
+9 V

aS
–

dr
+
–9 V

an
VOUT
VIN R1

Ch
jit
Sa
Fig. 9.1
by

(a) State
ed

(i) the name of this type of amplifier circuit,

ng

.............................................................................................................................. [1]
rra

(ii) the gain G in terms of resistances R1 and R2.

.............................................................................................................................. [1]
ea
dr
d an
le
m pi
Co

© UCLES 2010 9702/41/O/N/10

 19

(b) The value of R1 is 820 Ω. The resistor of resistance R2 is replaced with a light-dependent For
resistor (LDR). Examiner’s
The input potential difference VIN is 15 mV. Use

Calculate the output potential difference VOUT for the LDR having a resistance of

(i) 100 Ω (the LDR is in sunlight),

k ya
ha
aS
dr
an
VOUT = ............................................. V [2]

Ch
(ii) 1.0 MΩ (the LDR is in darkness).

jit
Sa
by
ed
ng

VOUT = ........................................... V [1]

rra
ea
dr
d an
le
m pi
Co

© UCLES 2010 9702/41/O/N/10 [Turn over

 20

10 (a) State three properties of an ideal operational amplifier (op-amp). For

Examiner’s
1. ...................................................................................................................................... Use

2. ......................................................................................................................................

3. ......................................................................................................................................

ya
[3]

k
(b) A circuit incorporating an ideal op-amp is to be used to indicate whether a door is open

ha
or closed.
Resistors, each of resistance R, are connected to the inputs of the op-amp, as shown in

aS
Fig. 10.1.

+3 V

dr
an
S R R
+9 V

Ch
–

jit
–9 V
Sa
R
R
by

R
ed
ng
rra

Fig. 10.1

The switch S is attached to the door so that, when the door is open, the switch is open.
ea

The switch closes when the door is closed.

dr
d an
le
m pi
Co

© UCLES 2010 9702/43/O/N/10

 21

(i) Explain why the polarity of the output of the op-amp changes when the switch For
closes. Examiner’s
Use

..................................................................................................................................

..................................................................................................................................

ya
..................................................................................................................................

k
.............................................................................................................................. [3]

ha
(ii) A red light-emitting diode (LED) is to be used to indicate when the door is open.

aS
A green LED is to indicate when the door is closed.

On Fig. 10.1,

dr
an
1. draw symbols for the LEDs to show how they are connected to the output of the
op-amp, [1]

Ch
2. identify the green LED with the letter G. [1]

jit
Sa
by

Please turn over for Question 11.

ed
ng
rra
ea
dr
d an
le
m pi
Co

© UCLES 2010 9702/43/O/N/10 [Turn over

 18

Section B For
Examiner’s
Answer all the questions in the spaces provided. Use

9 (a) An operational amplifier (op-amp) may be used as a comparator.

State the function of a comparator.

a
ky
..........................................................................................................................................

ha
..........................................................................................................................................

aS
...................................................................................................................................... [2]

(b) The variation with temperature θ of the resistance R of a thermistor is shown in Fig. 9.1.

dr
4.0

an
Ch
3.0

R / kΩ
jit
Sa
2.0
by
ed

1.0
ng
rra

0
0 5 10 15 20 25 30
a
re

θ / °C
Fig. 9.1
nd
da
le
pi
m
Co

© UCLES 2011 9702/41/M/J/11

 19

The thermistor is connected into the circuit of Fig. 9.2. For

Examiner’s
+5 V Use

X 2.0kΩ
+9 V

a
–

ky
+

ha
–9V

aS
2.0kΩ V OUT

dr
an
Fig. 9.2

Ch
The op-amp may be considered to be ideal.

(i) The temperature of the thermistor is 10 °C.

jit
Sa
Determine the resistance of the variable resistor X such that the output potential
VOUT is zero.
by
ed
ng
a rra
re

resistance = ............................................ Ω [2]

nd

(ii) The resistance of the resistor X is now held constant at the value calculated in (i).
Describe the change in the output potential VOUT as the temperature of the
thermistor is changed from 5 °C to 20 °C.
da

..................................................................................................................................
le

..................................................................................................................................
pi
m

..................................................................................................................................
Co

..................................................................................................................................

.............................................................................................................................. [4]

© UCLES 2011 9702/41/M/J/11 [Turn over

 20

Section B For
Examiner’s
Answer all the questions in the spaces provided. Use

9 (a) Describe the structure of a metal wire strain gauge. You may draw a diagram if you
wish.

a
ky
ha
aS
dr
an
..........................................................................................................................................

Ch
..........................................................................................................................................

jit
..........................................................................................................................................
Sa
.................................................................................................................................... [3]

(b) A strain gauge S is connected into the circuit of Fig. 9.1.

by

+4.5 V
ed

RF
strain
ng

gauge S
+9 V
rra

R
–
R
a

+
re

–9 V
V1
nd

VOUT
1.0 kΩ V2 RF
da
le
pi

Fig. 9.1
m

The operational amplifier (op-amp) is ideal.

Co

The output potential VOUT of the circuit is given by the expression

RF
VOUT = × (V2 – V1).
R

RF
(i) State the name given to the ratio
R.

............................................................................................................................ [1]
© UCLES 2011 9702/42/M/J/11
 21

(ii) The strain gauge S has resistance 125 Ω when not under strain. For
Calculate the magnitude of V1 such that, when the strain gauge S is not strained, Examiner’s
the output VOUT is zero. Use

a
ky
ha
aS
V1 = ........................................... V [3]

dr
(iii) In a particular test, the resistance of S increases to 128 Ω. V1 is unchanged.

an
R
The ratio F is 12.
R

Ch
Calculate the magnitude of VOUT .

jit
Sa
by
ed
ng

VOUT = ........................................... V [2]

a rra
re
nd
da
le
pi
m
Co

© UCLES 2011 9702/42/M/J/11 [Turn over