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QUESTION: 1

The driving point admittance of the network shown below is

Solution:

∴

QUESTION: 2

Figure shown below represents a d.c. 10 V voltage source as well as a 10 V a.c. 50 Hz voltage source while Z_{1} and Z_{2} are two unknown impedances. When Z_{1} is connected across 10V d.c. source, it draws a current of 10 A while it draws a current of 8 A if connected across 10V a.c. source.

Now, when Z_{2} is connected across 10 V d.c. source, it does not draw any current while it draws a current of 5 A if connected across 10 V a.c. source.

Q. What are the elements in Z_{1} and Z_{2}?

Solution:

When Z_{1} is connected across d.c. source, it draws 10 A current.

Again, when Z_{1} is connected across a.c. source, it draws 8 A.

Thus,

Thus, Z_{1} = (1 + j0.75) Ω

Now, when Z_{2} is connected across 10 V d.c. source, it doesn’t draw any current. Hence, Z_{2} must be a capacitor which wilt act as open circuit for d.c. source.

Also, Z_{2} draws 5 A when connected to 10 V a.c. source.

or,

Thus, Z_{2} = -j2 Ω

QUESTION: 3

The current through the capacitor in the given circuit is

Solution:

Since two voltage sources are present, we apply. Superposition theorem to find current through the capacitor i.e. current through -j5 Ω, reactance.

Here,

and

So,

QUESTION: 4

A parallel RLC circuit is said to be underdamped when

Solution:

The characteristic equation of a parallel RLC circuit is

Also,

Thus,

and

for underdamped circuit, ξ < 1

QUESTION: 5

Assertion (A): A coil, when connected across 230 V dc supply, will draw more current in comparison to that when connected across 230 V ac supply.

Reason (R): The inductance of the coil opposes the flow of alternating current (not that of direct current).

Solution:

QUESTION: 6

A two terminal black box contains one of the R-L-C elements. When the black box is connected to a 220 V ac supply, the current through the source is I. When a capacitance of 0.1 F is inserted in series between the source and the box, the current through the source is 2I. The element is

Solution:

As current is increased therefore, new impedance should reduce. If the unknown element will be inductive, the new impedance will be (X_{L}- X_{C}) Ω, so that the new value of current will increase.

QUESTION: 7

A system function has a pole at s = 0 and zero at s = -1. The constant multiplier is unity. For an excitation cost, the steady state response is given by

Solution:

Thus,

QUESTION: 8

For the a.c. circuit given below, what is the value of I?

Solution:

So,

QUESTION: 9

Consider the following pole-zero diagram of a system,

What will be the magnitude of the voltage phasor for i(t) = sin*t*?

Solution:

From the pole-zero plot,

(Since sint = i(t); ω = 1 rad/s)

so,

QUESTION: 10

A coil takes a current of 1∠60° A (lag) from a 100 V, 50 Hz supply. The resistance of the coil is

Solution:

Also,

or, cos 60° = R/100

or, R = 100 cos 60°

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