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

Question 9

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

Fig. 9.1

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

(ii) Explain what is meant by a virtual earth. [3]

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

(i) Calculate, for the LDR in bright sunlight, the voltmeter reading. [3]

(ii) The sunlight incident on the LDR becomes less bright.

State and explain the effect on the voltmeter reading of this decrease in brightness. [3]

Reference: Past Exam Paper – June 2010 Paper 41 Q9

Solution:

(a) (i)

point X shown correctly

(ii)

The open-loop gain of the op-amp is very large (or infinite gain).

The non-inverting input (V⁺) is at 0 V (since it is connected to earth).

For the amplifier not to saturate, the inverting input (V^-) must be almost equal to the potential of the non-inverting input (which is at 0 V).

So, the potential of the inverting input at said to be at virtual earth.

(b)

(i)

{Total input resistance = 1.0 + 0.2 = 1.2 kΩ}

total input resistance = 1.2 kΩ 

{For an inverting amplifier, gain = - R_F / R_IN }

(amplifier) gain (= –4.2 / 1.2) = –3.5 

{Gain = V_OUT / V_IN

V_OUT = Gain × V_IN = -3.5 × -1.5}

(voltmeter) reading = –3.5 × –1.5 = 5.25 V

(ii)

(The light is less bright so,) the resistance of the LDR increases

{This decreases the total input resistance.

Since gain = - R_F / R_IN, the gain of the amplifier decreases.}

(the amplifier) gain decreases

(so, the voltmeter) reading decreases