The current gain $\beta$ may be defined as
A) The ratio of change in collector current to the change in emitter current for a constant collector voltage in a common base arrangement.
B) The ratio of change in collector current to the change in the base current at constant collector voltage in a common emitter circuit.
C) The ratio of change in emitter current to the change in base current for constant emitter voltage in common emitter circuits.
D) The ratio of change in base current to the change in collector current at constant collector voltage in common emitter circuits.

Hint: In order to solve this question, firstly we will understand the concept of current gain $\beta $ i.e. $ \dfrac{{{I_C}}}{{{I_B}}}$. Then we will compare the given options to get the required answer.

Complete Step-by-Step solution:
The input signal between the base and the emitter is applied in the Typical Emitter or grounded emitter configuration, while the output is taken from between the collector and the emitter. This type of configuration is the most commonly used circuit for transistor-based amplifiers and represents the normal method for connecting bipolar transistors.
In a common emitter amplifier circuit, the current flowing out of the transistor must be equal to the currents flowing into the transistor. As the load resistance $\left( {{R_L}} \right)$ The current gain of the typical emitter transistor configuration is very high as it is the ratio of the collector in series i.e.$\dfrac{{{I_C}}}{{{I_B}}}$. A transistors current gain is given by Beta $\beta $.
Current gain $\beta $ is defined as the ratio of change in collector current to change in base current for a constant collector voltage in a common emitter circuit.
$\beta = \dfrac{{\Delta {i_c}}}{{\Delta {i_B}}}$
Or we can rewrite it as $\beta = \dfrac{{{I_c}}}{{{I_B}}}$.
Then minor variations in the current flow in the base will regulate the current in the circuit of the emitter-collector. Generally, $\beta $ has value between 20 and 200 for transistors for general purpose. So if a transistor has a beta value of say 100, then for every 100 electrons flowing between the emitter-collector terminal, one electron will flow from the base terminal.
And we infer the current gain $\beta $ is the ratio of change in collector current to change in base current for a constant collector voltage in a common emitter circuit.
Hence, option B is correct.

Note- While solving this question, we must know that the emitter current is a combination of the collector AND the base current combined, In this type of transistor configuration the load resistance also has both the collector current and the input current. And we'll get our desired outcome.