Signals and Systems - Online Test
Q1.
Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding star equivalent will be scaled by a factor of
Answer : Option B
Explaination / Solution:
In the equivalent star connection, the resistance can be given as
Q2. A continuous-time function x(t) is periodic with period T. The function is sampled uniformly
with a sampling period TS. In which one of the following cases is the sampled signal periodic?
Answer : Option B
Explaination / Solution:
Q3. The circuit shown below is driven by a sinusoidal input Vi = Vpcos(t/RC). The
steady state output vo
Answer : Option A
Explaination / Solution:
parallel combination of R and C equivalent impedance is
Transfer function can be written as
Q4. Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh‟s Table of the system characteristic equation
X: The system is stable … P: … when all elements are positive
Y: The system is unstable … Q: … when any one element is zero
Z: The test breaks down … R: … when there is a change in sign of coefficients
Answer : Option D
Explaination / Solution:
No Explaination.
Q5. The transfer function 
Answer : Option D
Explaination / Solution:
For the given capacitance, 
in the circuit, we have the reactance.
in the circuit, we have the reactance.
Q6. A first-order low-pass filter of time constant T is excited with different input signals (with zero
initial conditions up to t = 0). Match the excitation signals X, Y, Z with the corresponding time
responses for t ≥ 0:
X: Impulse P: 1 – e-t/T
Y: Unit step Q: t – T(1 – e(-t/T)
Z :Ramp R: e-t/T
Answer : Option C
Explaination / Solution:
In general the first order, L.P.F filter transfer function is 
because G(0) = k and G(∞) = ∞ if we take this transfer function as reference and give different input such as
s(t).r(t).u(t)
because G(0) = k and G(∞) = ∞ if we take this transfer function as reference and give different input such as
s(t).r(t).u(t)
Q7. A source 
has an internal impedance of 
If a purely resistive load connected to this source has to extract the maximum power out of the source, its value inΩ should be
has an internal impedance of If a purely resistive load connected to this source has to extract the maximum power out of the source, its value inΩ should be
Answer : Option C
Explaination / Solution:
For the purely resistive load, maximum average power is transferred when
where
is the equivalent thevinin (input) impedance of the circuit. Hence,
we obtain
where
is the equivalent thevinin (input) impedance of the circuit. Hence,we obtain
Q8. The impulse response of a continuous time system is given by 
The value of the step response at t = 2 is
The value of the step response at t = 2 is
Answer : Option B
Explaination / Solution:
Q9. In the circuit shown below, the Norton equivalent current in amperes with
respect to the terminals P and Q is
Answer : Option A
Explaination / Solution:
Replacing P - Q by short circuit as shown below we have
Using current divider rule the current ISC is
Q10. In the circuit shown below, the value of RL such that the power transferred to RL is maximum is
Answer : Option C
Explaination / Solution:
Power transferred to RL will be maximum when RL is equal to the thevenin
resistance. We determine thevenin resistance by killing all source as follows :
