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Question 617: [Operational Amplifier Circuits]

Amplifier circuit incorporating an operational amplifier (op-amp) shown in Fig.1.

(a) State

(i) name of this type of amplifier circuit

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

(b) Value of R₁ is 820 Ω. The resistor of resistance R₂ is replaced with light-dependent resistor (LDR).

Input potential difference V_IN is 15mV.

Calculate output potential difference V_OUT for LDR having a resistance of

(i) 100Ω (LDR is in sunlight)

(ii) 1.0MΩ (LDR is in darkness)

Reference: Past Exam Paper – November 2010 Paper 41 & 42 Q9

Solution 617:

(a)

(i) Non-inverting (amplifier)

(ii) Gain G = 1 + R₂/R₁

(b)

(i)

Gain = 1 + 100/820 (= 1.12)  

(Gain = V_OUT/V_IN)

Output = (Gain x V_IN = 1.12x15 =) 17mV

(ii)

{Gain = 1 + [(1x10⁶)/820] = 1220

Output = Gain x V_IN = 1220 x 15 = 18397 mV = 18V

But the input supply line is only 9V. So, the op-amp saturates. The output is thus 9V (equal to the input supply line)}

Output = 9V  

Question 618: [Modulation]

(a) Radio communication may be either frequency modulated or amplitude modulated. Explain what is meant by modulation.

(b) Amplitude-modulated radio wave is to be used for broadcast of music having frequencies between 30 Hz and 4500 Hz. Radio station is broadcasting in the long wave waveband (wavelengths between 1 × 10³ m and 1 × 10⁴ m).

Determine

(i) bandwidth of the broadcast,

(ii) maximum number of radio stations that could operate simultaneously in the same area within the long wave waveband.

(c) On axes of Fig.1, sketch graph of a typical power spectrum for the radio station in (b).

Label the x-axis with values of frequency.

Reference: Past Exam Paper – November 2006 Paper 6 Q15

Solution 618:

(a) Modulations are variations in either the amplitude or the frequency of a wave

EITHER in synchrony with the displacement of information signal

OR in order to carry information on the wave

(b)

(i)

{The bandwidth is twice the (maximum) audio frequency.}

Bandwidth of the broadcast = 9 kHz

(ii).

The LW (long wave) frequency range is 30 kHz → 300 kHz

{The bandwidth of 1 broadcast (used by 1 station) is 9 kHz as stated above. Now, the frequencies of the long wave waveband varies from 30 kHz → 300 kHz. So, 1 station could use frequencies 30 kHz to 38 kHz (there’s actually 9 here: 30, 31, 32, 33, 34, 35, 36, 37 and 38), another 39 kHz to 47 kHz, etc …

To find the maximum number of stations, we take (300 – 30) / 9}

Number of stations = 270 / 9 = 30

(c)

For the sketch, the carrier frequency should be shown as a vertical line and two sidebands. There should be a reasonable symmetry with the sideband indicating approx. 4500 Hz range.

{Note that the carrier frequency has be chosen between the range of 30 kHz and 300 kHz. (Of course, 30 kHz would not work because one of the sidebands would be outside the range.) The sidebands should each be shown 4500 Hz away from the carrier frequency.}

Question 619: [Electric Potential]

(a) Define electric potential at a point.

(b) Isolated solid metal sphere is positively charged.

Variation of the potential V with distance x from the centre of the sphere is shown in Fig.1.

Use Fig.1 to suggest

(i) why radius of the sphere cannot be greater than 1.0 cm,

(ii) that charge on the sphere behaves as if it were a point charge.

(c) Assuming that charge on the sphere does behave as a point charge, use data from Fig.1 to determine the charge on the sphere.

Reference: Past Exam Paper – November 2014 Paper 41 & 42 Q5

Solution 619:

Go to
An isolated solid metal sphere is positively charged. The variation of the potential V with distance x from the centre of the sphere is shown in  Fig. 5.1.

Question 620: [Forces]

Two co-planar forces act on rim of a wheel. The forces are equal in magnitude.

Which arrangement of forces provides only a couple?

Reference: Past Exam Paper – November 2011 Paper 12 Q13

Solution 620:

Answer: D.

The system of forces can be provide both a resultant force and a resultant torque. We need only a couple, so the resultant force should be zero.

For the resultant force to be zero, the direction of the 2 forces should oppose each other. [A, B and C are incorrect]

A couple on an object consists of 2 equal forces acting in opposite directions to each other, they act through 2 different points, in such a way that they produce a turning effect.

E.g. steering wheel in a car