Consider the networks shown in the following figures (a) and (b) : The above networks are :
Reciprocal network of each other
To determine the relationship between the two given networks in figures (a) and (b), let's analyze the properties that define reciprocal networks.
A reciprocal network is one where the transfer impedance is symmetric, meaning that if you apply a voltage in one direction and observe the resulting current, you'll get the same result if you swap the positions of the voltage and current sources. Mathematically, this condition is represented as:
\(Z_{12} = Z_{21}\)
In figure (a), the input is provided by a source \(V_1 = V_S\), leading to current \(I_1\) entering the network and \(I_2\) exiting it at the far side. Likewise, in figure (b), the roles of input and output are reversed which means:
- The source is now \(V_2 = V_S\), leading to a new current \(I'_1\) in place of \(I_2\) from the first figure.
By checking whether these configurations give equivalent responses from the network, if the transfer functions across both configurations are equal or symmetric, the networks are reciprocal.
According to the properties of reciprocal networks and the explained figures, the circuit configurations ensure that:
\(Z_{12} = Z_{21}\)
Therefore, the correct answer is that the given networks are Reciprocal network of each other. This is supported by the symmetry in their configurations as they sustain the reciprocal property by swapping source and output.
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