Circuit Laws & Theorems

A nullator is defined as a circuit element where the voltage across the device and the current through the device are both zero. A series combination of a nullator and a resistor of value, $R$, will behave as a

A benchtop dc power supply acts as an ideal 4 A current source as long as its terminal voltage is below 10 V. Beyond this point, it begins to behave as an ideal 10 V voltage source for all load currents going down to 0 A...

In a linear two-port network, when 10 V is applied to Port 1, a current of 4 A flows through Port 2 when it is short-circuited. When 5V is applied to Port1, a current of 1.25 A flows through a 1 Ω resistance connected ac...

A non-ideal voltage source V S has an internal impedance of Z S . If a purely resistive load is to be chosen that maximizes the power transferred to the load, its value must be

An incandescent lamp is marked 40W, 240V. If resistance at room temperature $$\left(26^\circ\mathrm C\right)\;\mathrm{is}\;120\mathrm\Omega$$ and temperature coefficient of resistance is $$4.5\;\times\;10^{-3}/^\circ C$$...

A source $$v_s\left(t\right)=V\cos100\mathrm{πt}$$ has an internal impedance of (4 + j3) Ω.If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should be

How many 200 W/200 V incandescent lamps connected in series would consume the same total power as a single 100 W/200 V incandescent lamp?

The matrix $$A$$ given below is the node incidence matrix of a network. The columns correspond to braches of the network while the rows correspond to nodes. Let $$V = {\left[ {{v_1}\,\,{v_2}....{v_6}} \right]^T}$$ denote...

A $$3$$ $$V$$ $$dc$$ supply with an internal resistance of $$2$$ $$\Omega $$ supplies a passive non-linear resistance characterized by the relation $${V_{NL}} = {{\rm I}^2}{}_{NL}$$. The power dissipated in the non-linea...

A $$3$$ $$V$$ $$dc$$ supply with an internal resistance of $$2\,\,\Omega $$ supplies a passive non-linear resistance characterized by the relation $${V_{NL}} = {\rm I}_{NL}^2.$$ The power dissipated in the non-linear res...

The graph of an electrical network has $$N$$ nodes and $$B$$ branches. The number of links, $$L$$, with respect to the choice of a tree, is given by

Two incandescent light bulbs of $$40$$ $$W$$ and $$60$$ $$W$$ rating are connected in series across the mains. Then

A current amplifier has an input resistance of $$10\Omega ,$$ an output resistance of $$10\,\,k\Omega $$ and a Current gain of $$1000.$$ It is feed by a current source having a source resistance of $$10$$ $$k\Omega $$ an...

When a periodic triangular voltage peak amplitude $$1$$ $$V$$ and frequency $$0.5$$ $$Hz$$ is applied to a parallel combination of $$1\,\Omega $$ resistance and $$1$$ $$F$$ capacitance, the current through the voltage so...

The colour code of a $$1k\Omega $$ resistance is

Currents $${{\rm I}_1},\,{{\rm I}_2}$$ and $${{\rm I}_3}$$ meet at a junction (node) in a circuit. All currents are marked as entering the node. If $${{\rm I}_1} = - 6\sin \left( {\omega t} \right)$$ $$mA$$ and $${{\rm I...

The mobility of an electron in a conductor expressed in terms of

When a resistor $$R$$ is connected to a current source, it consumes a power of $$18$$ $$W.$$ when the same $$R$$ is connected to a voltage source having the same magnitude as the current source, the power absorbed by $$R...

A $$10$$ $$V$$ battery with an internal resistance of $$1\,\Omega $$ is connected across a nonlinear load whose $$V-1$$ characteristic is given by $$7{\rm I} = {V^2} + 2V.$$ The current delivered by the battery is .........

Superposition principle is not applicable to a network containing time-varying registors.