GATE 2021 Electric Circuits Questions and Solutions

Consider the circuit shown in the figure. The value of \(v_o\) (rounded off to one decimal place) is ____ V.

Solution

Use nodal analysis at the node whose voltage is \(V_o\), with resistances in k\(\Omega\) and currents in mA. The 6 mA source drives current into the node; the two 1 k\(\Omega\) branches carry \((V_o - 4)\) and \(V_o\) out of it; the branch on the right carries the 6 mA and 2 mA source currents, \(6 + 2 = 8\) mA, out of it.

KCL at \(V_o\) (sum of currents leaving = 0):

The condition for maximum power transfer to a load impedance \(Z_L = R_L + jX_L\) from a source with internal impedance \(Z_S = R_S + jX_S\) is:

1. \(R_L = R_S\) and \(X_L = X_S\)
2. \(R_L = R_S\) and \(X_L = -X_S\)
3. \(R_L = |Z_S|\) and \(X_L = 0\)
4. \(Z_L = R_S\)

Solution

• For a complex source impedance, maximum power is transferred when the load impedance is the conjugate of the source impedance, i.e., \(Z_L = Z_S^*\).

A two-port network is reciprocal if its admittance parameters satisfy which of the following conditions?

1. \(y_{11} = y_{22}\)
2. \(y_{12} = -y_{21}\)
3. \(y_{12} = y_{21}\)
4. \(y_{11}y_{22} - y_{12}y_{21} = 1\)

Solution

• A two-port network is considered reciprocal if the ratio of the output current (Port 2) to the input voltage (Port 1) equals the ratio of the input current (Port 1) to the output voltage (Port 2) under appropriate open/short circuit conditions. In terms of the Y-parameters (Admittance parameters), this condition is \(y_{12} = y_{21}\).
• The condition \(y_{11} = y_{22}\) indicates a symmetric network.