Open loop gain of an amplifier can be represented by the formula
A. $\dfrac{{{V_0}}}{{{V_i}}}$
B. ${V_0} + {V_i}$
C. ${V_0} - {V_i}$
D. ${V_0} \times {V_i}$

Hint: If we combine two extrinsic semiconductors we get diodes. Extrinsic semiconductor in which electrons are excess are called n-type semiconductor whereas extrinsic semiconductor in which holes are excess are called p-type semiconductor. Now if we combine two diodes we get a transistor. It can be a p-n-p transistor or n-p-n transistor. That transistor has emitter base and collector and can be used as switches, amplifiers and as many other devices

Complete step by step solution:
The characteristics of emitter, base and collector will be different. Emitter is highly doped while the collector and base are lightly doped. The width of the base is very less. Moreover emitter-base junction is always forward biased whereas base-collector junction is always reverse biased. Forward biased in the sense diode provides very low resistance and reverse biased in the sense diode provides huge resistance.
The voltage which we applied will be lesser than the output voltage. That means there will be some voltage gain. That voltage gain depends upon the load resistance and the input resistance.
An ideal amplifier will be having high input impedance and very low output impedance. It should not draw any current from the input
Let the output voltage be ${V_0}$ and the input voltage that is being amplified be ${V_i}$
Gain in the amplifier can be given as
$A.G = \dfrac{{{V_0}}}{{{V_i}}}$
That is the ratio of output voltage to the input voltage.

Hence, option A is the correct answer.

Note:
Usually in electronic circuits we give some input voltage to attain the required output. After getting the output we will check if the output we had got is expected one or not. This is called taking the feedback and when feedback is taken it is closed loop. If feedback is not taken then it is called open loop.