Figure shows as electronic voltage regulator the zener diode may be assumed to require a minimum current of $$25$$ $$mA$$ for satisfactory operations. The value of $$R$$ required for satisfactory voltage regulation of the circuit is

Figure shown below shows a common emitter amplifier. The quiescent collector voltage of the circuit is approximately.

With the ideal operational amplifiers, the circuit in figure simulates the equation

In the figure shown, assume that the zener diode and operational amplifier to be ideal.

$$(a)$$ Draw the equivalent circuit and evaluate the gain $$\left( {{V_0}\,\,vs\,\,{V_i}} \right)$$ of the circuit for

$$(i)$$ $${V_i} \le 0$$ $$\,\,\,\,\,\left( {ii} \right)\,\,\,0 < {V_i} < 5V\,\,\,\,\,\,$$ $$\,\,\,\,\,\left( {iii} \right)\,\,\,{V_i} > 5V\,\,\,\,\,\,$$

$$(b)$$ Sketch the gain $$\left( {{V_0}\,\,\,{V_s}\,\,\,{V_i}} \right)$$ characteristics of the above circuit and label the salient features.

Figure shows a common emitter amplifier

$$(a)$$ Simplify the circuit by applying thevenin's theorem to biasing network $${R_1},{R_2}$$ at
$$\,\,\,\,\,\,\,$$ the base of the transistor.
$$(b)$$ Assuming $${C_s}$$ to be a short for frequency range considered. Draw the small signal
$$\,\,\,\,\,\,\,$$ $$a.c.$$ model of the circuit obtained in $$(a)$$ by using the simple model for the
$$\,\,\,\,\,\,\,$$ transistor shown in figure.
$$(c)$$ Evaluate the small signal gain $$\left( {{{{V_0}} \over {{V_i}}}} \right)$$ of the amplifier.

Which of the following is the transfer function of a system having the Nyquist plot shown in Fig. below.

A unity feedback system has an open-loop transfer function of the form $$KG\left( s \right) = {{K\left( {s + a} \right)} \over {{s^2}\left( {s + b} \right)}};\,\,\,\,b > a$$ Which of the loci shown in Fig. can be valid root-loci for the system?

The system having the Bode magnitude plot shown in Fig. below has the transfer function

The signal flow graph of Fig. shown below, has ___________ forward paths / and ________feed - back loops.

A first order system and its response to a unit step input are shown in Fig. below. The system parameters are
$$a=$$ ____________
$$K=$$ ___________

A unity feedback system has the forward loop transfer function $$G\left( s \right) = {{K{{\left( {s + 2} \right)}^2}} \over {{s^2}\left( {s - 1} \right)}}$$

(a) Determine the range of $$K$$ for stable operation

(b) Determine the imaginary axis crossover points

(c) Without calculating the real axis break - away points, sketch the form of root loci for the system.

An under damped second order system having a transfer function of the form $$M\left( s \right) = {{k\omega _n^2} \over {{s^2} + 2\zeta {\omega _n}s + \omega _n^2}}\,\,$$ has frequency response plot shown in Fig. below, then the system gain $$K$$ is __________ and the damping factor is approximately _______

The current $$i(t)$$ passing through $$10\Omega $$ resistor as shown in fig $$A$$. as a waveform as shown in fig $$B.$$ Then the reading of the d.c voltmeter is connected across $$10\Omega $$ resistor is