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
Which of the following Is not true for a series RLC resonant circuit?
When Δω increases, selectivity decreases and viceversa.
Also, V_{c}_{max} occurs at,
The halfpower 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
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
For the tank circuit shown below, the circulating current at resonance is given by
At resonance, X_{L} = X_{C}
∴ I_{L} = I_{C} (for parallel resonant circuit)
Hence,
or,
or,
(I_{L}=I_{C} = circulating current)
The value of R_{C} in the circuit shown below to yield resonance will be
Here,
At resonance,
Img [Y] = 0
or,
A resonating circuit has 10ft resistance, if the supply is 10 Ω, the power at half power frequency will be
At resonance,
Now, power at half power frequency
For the circuit shown below, what are the values of R_{1}, and R_{2} so that the circuit will resonate at all frequencies?
For the given circuit to resonate at all frequency,
Note: Resonant frequency of given circuit is
Thus,
The value of current I_{1} in the circuit shown below is
Since X_{L} = X_{L}, therefore given circuit will be at resonance
∴ I_{1 }= 100/5 = 20 A
The transfer function of the network shown below is
The given circuit in sdomain is shown below.
Now,
and
So,
or,
The poles and zeros of the transfer function for the circuit shown below are located at
or,
or,
Thus, there is nozero 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
The output of a linear system for a unit step input is given by t^{2} e^{t}. The transfer function is given by
Given, C(t) = t^{2}e^{t}
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
Resonant frequency,
Also,
When f = 0, ω = 0 and z = 0.
When f = ∞, co = ∞ and z= 0.
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
ListII
1. 0 → f_{2}, f_{1} → ∞
2. f_{c} → ∞
3. f_{1} → f_{2}
4. 0 → f_{c}
Codes:
The transfer function is for an active
When s → 0 , H (0) → 0
When s → ∞, H(∞) → 0
Hence, given T.F. is for a band pass filter.
Match List I (Transfer function) with List II (Type of filter) and select the correct answer using the codes given below the lists:
Codes:
Putting s → 0 and s → ∞ we can find the type of the filter.
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