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QUESTION: 1

A series RLC circuit consist of resistance of 10 ohms, an inductance of 0.1 H and a capacitance of 0.001 μF. The frequency at resonance is

Solution:

QUESTION: 2

Which of the following Is not true for a series RLC resonant circuit?

Solution:

When Δω increases, selectivity decreases and vice-versa.

Also, V_{c}|_{max} occurs at,

QUESTION: 3

The half-power frequencies of a series resonant circuit where the resonant frequency is 150 x 10^{3} Hz and the bandwidth is 75 kHz will be respectively given by

Solution:

Given, Δf = 75 kHz = f_{2} - f_{1...}(i)

On solving equations (i) and (ii), we get

f_{1 }= 117 kHz and f_{2} = 192 kHz

QUESTION: 4

For the tank circuit shown below, the circulating current at resonance is given by

Solution:

At resonance, X_{L} = X_{C}

∴ I_{L} = I_{C} (for parallel resonant circuit)

Hence,

or,

or,

(I_{L}=I_{C} = circulating current)

QUESTION: 5

The value of R_{C} in the circuit shown below to yield resonance will be

Solution:

Here,

At resonance,

Img [Y] = 0

or,

QUESTION: 6

A resonating circuit has 10ft resistance, if the supply is 10 Ω, the power at half power frequency will be

Solution:

At resonance,

Now, power at half power frequency

QUESTION: 7

For the circuit shown below, what are the values of R_{1}, and R_{2} so that the circuit will resonate at all frequencies?

Solution:

For the given circuit to resonate at all frequency,

Note: Resonant frequency of given circuit is

Thus,

QUESTION: 8

The value of current I_{1} in the circuit shown below is

Solution:

Since X_{L} = X_{L}, therefore given circuit will be at resonance

∴ I_{1 }= 100/5 = 20 A

QUESTION: 9

The transfer function of the network shown below is

Solution:

The given circuit in s-domain is shown below.

Now,

and

So,

or,

QUESTION: 10

The poles and zeros of the transfer function for the circuit shown below are located at

Solution:

or,

or,

Thus, there is no-zero for T.F.

Poles are at:

2s^{2} + 200s + 1 = 0

or,

or,

= -100 ±99.99

= 0 or -200

Hence, poles are at: s = 0, -200

QUESTION: 11

The output of a linear system for a unit step input is given by t^{2} e^{-t}. The transfer function is given by

Solution:

Given, C(t) = t^{2}e^{-t}

QUESTION: 12

A constant voltage but variable frequency ac source feeds L and C in parallel as shown below:

The impedance seen by source is Z

1. Z is zero when f = 0.

2. Z is zero when f = infinity.

3. Z is infinite when f = 0.

4. Z is infinite when f = infinity.

5. resonant frequency,

From above, the correct answer is

Solution:

Resonant frequency,

Also,

When f = 0, ω = 0 and z = 0.

When f = ∞, co = ∞ and z= 0.

QUESTION: 13

Match List- I (Types of filters) with List- II (Attenuation band) and select the correct answer using the codes given below the lists:

List -I

A. Low pass

B. High pass

C. Band pass

D. Band stop

List-II

1. 0 → f_{2}, f_{1} → ∞

2. f_{c} → ∞

3. f_{1} → f_{2}

4. 0 → f_{c}

Codes:

Solution:

QUESTION: 14

The transfer function is for an active

Solution:

When s → 0 , H (0) → 0

When s → ∞, H(∞) → 0

Hence, given T.F. is for a band pass filter.

QUESTION: 15

Match List- I (Transfer function) with List- II (Type of filter) and select the correct answer using the codes given below the lists:

Codes:

Solution:

Putting s → 0 and s → ∞ we can find the type of the filter.

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