Test: ESE Electrical - 3 - Electrical Engineering (EE) MCQ

This 0.2 V increases linearly from 0 to 0.2 V. Then current is zero. So capacitor hold this voltage.

 

= 600 mA
For 1 ms < t < 2 ms, 

Number of junction points for the above circuit is 6

⇒ 

⇒ 

In differential equation putting t = 0 and sovling

I₁ = (V₁ - V₂) Y_ab + V₁Y_ab 
⇒ I₁ = V₁(Y_a + Y_ab) - V₂Y_ab .....(i)
I₂ = (V₂ - V₁)Y_ab + V₂Y_b = -V₁Y_ab + V₂(Y_b + Yab) .....(ii)

As the load impedance is Z∠Ø, the current flows in the three load impedances and the current flowing in the Y impedance is I_Y = V_YB∠120⁰/Z∠Ø = (V/Z)∠-120-Ø.

The line current I₁ is the difference of I_R and I_B. So the line current I₁ is I₁ = I_R – I_B = (51.96 + j10) A.

F = q1q2/(4∏εor²) = -2 X 9/(10^-9 X 12) = -18 X 10⁹.

Since the charges are unlike, the force will be attractive. Thus the force directs from 1C to -4C.

Because f_s ≤ 2f₀,

Ts ≤ _.

Since the ROC includes the z = 3/4, ROC is

Since X(z) converges on |z| = 1. So ROC must include this circle.

y[n] is shown is fig.

It has fundamental period of 10.

Concept:
Multiplication in the time domain is the convolution in the frequency domain and the maximum frequency of convolution of the signal is the sum of individual frequencies, i.e.
If z(t) = x(t) y(t)
The maximum frequency of Z(ω) = ω_x + ω_y
where ω_x is the maximum frequency of signal x(t)
ω_y is the maximum frequency of signal y(t)
Application:
The maximum frequency present in x(t) is:

Similarly, the maximum frequency present in y(t) is:

Now, the maximum frequency present in z(t) = x(t) y(t) will be:
f_z = f_x + f_y
f_z = 250 kHz
Nyquist sampling frequency will now be:
f_N = 2 × f_z
f_N = 500 kHz

Given g(n) is a real valued 2N point sequence. The 2N point sequence is divided into two N point sequences x1(n) and x2(n)
Let x(n)= x1(n)+jx2(n)
=> X1(k)= 1/2 [X*(k)+X*(N-k)] and X2(k)= 1/2j [X*(k)-X*(N-k)] We know that g(n)= x1(n)+x2(n)
=>G(k)= X1(k)+W₂^kNX2(k), k=0,1,2…N-1.

When h(n)=-h(M-1-n) and M is even, we know that H(0)=0. Thus it is not used in the design of a low pass linear phase FIR filter.

We know that if h(n)=-h(M-1-n) and M is odd, we get H(0)=0 and H(π)=0. Consequently, this is not suitable as either a low pass filter or a high pass filter and when h(n)=-h(M-1-n) and M is even, we know that H(0)=0. Thus it is not used in the design of a low pass linear phase FIR filter. Thus the anti-symmetric condition is not used in the design of low pass linear phase FIR filter.

The phenomena of 'limit cycles' and 'jump resonance' are observed in non-linear systems.

Limit cycles refer to a recurring pattern of behavior in a dynamic system, where the system's state variables repeat themselves over time. In non-linear systems, limit cycles can arise due to the interactions between various system components and their non-linear characteristics.

Jump resonance, also known as bifurcation or sudden change in behavior, occurs in non-linear systems when a small change in a parameter or input leads to a significant and abrupt change in the system's response.

Linear systems, option (A), typically do not exhibit limit cycles or jump resonance since they follow predictable and proportional relationships between inputs and outputs. Distributed systems, option (B), refer to systems that are spread across multiple interconnected components, but the presence of limit cycles or jump resonance is not specific to distributed systems.

Discrete time systems, option (D), involve systems where the variables are updated at discrete time intervals. While discrete time systems can exhibit complex behavior, the presence of limit cycles and jump resonance is more commonly associated with continuous-time non-linear systems.

Therefore, the correct answer is option (C) non-linear systems. Limit cycles and jump resonance are observed in non-linear systems due to their inherent complexity and interactions between system components.

On shifting the take-off point beyond block G, we have the reduced block diagram as shown below:

On further reducing the above block diagram, we get the block diagram as shown below.

Delay time (t_d) is the time required for the response curve to reach 50% of the final value.

The characteristic equation is,
1 + G(s)H(s) = 0 

The Routh's array is:

For absolute stability, we have:

Addition of real pole to an open loop T.F. decreases the stability because root locus shifts towards right of s-plane. Hence, assertion is a false statement.

At gain crossover frequency 
∴ Gain in dB = 20 log |G(jω|
= 20 log 1 = 0 dB