Series-Parallel Connection:

When two networks are connected in series-parallel connection, it means that one network is connected in series with the other network, and the resulting combination is connected in parallel with another network. This type of connection is commonly used in electrical circuits to achieve desired circuit characteristics.

Forward Short-Circuit Current Gain:

The forward short-circuit current gain, denoted by h_fe, is a parameter used to describe the amplification properties of a transistor in a common-emitter configuration. It represents the ratio of the change in collector current to the change in base current, while keeping the collector-emitter voltage constant.

Matrix Representation of Networks:

The Z-parameters and h-parameters are matrix representations commonly used to describe the behavior of electrical networks. The Z-parameter matrix (also known as impedance matrix) represents the relationship between the voltages and currents at the input and output ports of a network, while the h-parameter matrix represents the relationship between the currents and voltages at the input and output ports of a network.

Calculation of Forward Short-Circuit Current Gain:

The forward short-circuit current gain of the network can be calculated by summing the h-parameter matrices of the individual networks connected in series-parallel.

When two networks are connected in series, the h-parameter matrices are multiplied together to obtain the overall h-parameter matrix of the combination.

Similarly, when two networks are connected in parallel, the h-parameter matrices are summed together to obtain the overall h-parameter matrix of the combination.

Therefore, when two networks are connected in series-parallel connection, the forward short-circuit current gain of the network is the sum of the h-parameter matrices of the individual networks connected in the combination.

Conclusion:

In conclusion, the correct answer is option B, which states that the forward short-circuit current gain of the network is the sum of the h-parameter matrices of the individual networks connected in series-parallel. This is because the h-parameters represent the relationship between the currents and voltages at the input and output ports of a network, and when two networks are connected in series-parallel, their h-parameter matrices are summed together to obtain the overall h-parameter matrix of the combination.