GATE Questions & Answers of Network Theorems: Superposition, Thevenin and Norton’s Maximum Power Transfer

In the circuit shown below,V_S is a constant voltage source and I_L is a constant current load.

The value of I_L that maximizes the power absorbed by the constant current load is

•  (A) $\frac{{\mathrm{V}}_{\mathrm{S}}}{4\mathrm{R}}$
•  (B) $\frac{{\mathrm{V}}_{\mathrm{S}}}{2\mathrm{R}}$
•  (C) $\frac{{\mathrm{V}}_{\mathrm{S}}}{\mathrm{R}}$
•  (D) $\infty$

In the given circuit, the maximum power (in Watts) that can be transferred to the load R_L is ____.

In the circuit shown, the Norton equivalent resistance (in Ω) across terminals a-b is ___________.

For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b is _____.

Norton’s theorem states that a complex network connected to a load can be replaced with an equivalent impedance

•  (A) in series with a current source
•  (B) in parallel with a voltage source
•  (C) in series with a voltage source
•  (D) in parallel with a current source

In the figure shown, the value of the current I (in Amperes) is __________.

In the circuit shown in the figure, the angular frequency ω (in rad/s), at which the Norton equivalent impedance as seen from terminals b-b′ is purely resistive, is _________.

The impedance looking into nodes 1 and 2 in the given circuit is

•  (A) 50$\Omega$
•  (B) 100$\Omega$
•  (C) 5 k$\Omega$
•  (D) 10.1 k$\Omega$

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

•  (A) 0.8$\Omega$
•  (B) 1.4$\Omega$
•  (C) 2$\Omega$
•  (D) 2.8$\Omega$

In the circuit shown below, the Norton equivalent current in amperes with respect to the terminals P and Q is

•  (A) 6.4 -j4.8
•  (B) 6.56 -j7.87
•  (C) 10 +j0
•  (D) 16 +j0

In the circuit shown below, the value of R_L such that the power transferred to R_L is maximum is

•  (A) 5Ω
•  (B) 10 Ω
•  (C) 15Ω
•  (D) 20 Ω

In the circuit shown, what value of R_L maximizes the power delivered to R_L?

•  (A) 2.4 Ω
•  (B) $\frac{8}{3}$ Ω
•  (C) 4 Ω
•  (D) 6 Ω

The Thevenin equivalent impedance Z_th between the nodes P and Q in the following circuit is

•  (A) 1
•  (B) $1+s+\frac{1}{s}$
•  (C) $2+s+\frac{1}{s}$
•  (D) $\frac{s^2+s+1}{s^2+2s+1}$

An independent voltage source in series with an impedance Z_S = R_S + jX_S delivers a maximum average power to a load impedance Z_L when

•  (A) Z_L = R_S + jX_S
•  (B) Z_L = R_S
•  (C) Z_L = jX_S
•  (D) Z_L = R_S - jX_S

For the circuit shown in the figure, the Thevenin voltage and resistance looking into X-Y are:

•  (A) 4/3 V, 2 Ω
•  (B) 4 V, 2/3 Ω
•  (C) 4/3 V, 2/3 Ω
•  (D) 4 V, 2 Ω