**Block diagram Algebra Objective Questions**

**1. Consider the block diagram shown below:**

**If the transfer function of the system is given by T(s)=G1G2+G2G3/1+X. Then X is:**

a) G2G3G4

b) G2G4

c) G1G2G4

d) G3G4

**Answer:** b

**Explanation:** Use the technique of making two different block diagram by dividing two summers and use the approaches of shifting take off point and blocks.

**2. For the block diagram given in the following figure, the expression of C/R is:**

a) G1G2G3/1-G2G1

b) G1G2/1-G1G2G3

c) G1G2G3/1-G1G2G3

d) G1G2/G3(1-G1G2)

**Answer:** a

**Explanation:** Block diagram is being converted into signal flow graphs by considering each take off point as a node and each forward transfer function as forward gain.

**3. The transfer function from D(s) to Y(s) is :**

a) 2/3s+7

b) 2/3s+1

c) 6/3s+7

d) 2/3s+6

**Answer:** a

**Explanation:** Y(s)/D(s)=2/3s+1/1+3*(2/3s+1)=2/3s+7.

**4. The closed loop gain of the system shown in the given figure is :**

a) -9/5

b) -6/5

c) 6/5

d) 9/5

**Answer:** b

**Explanation:** C(s)/R(s)=-3/1+3/2=-6/5.

**5. The advantage of block diagram representation is that it is possible to evaluate the contribution of each component to the overall performance of the system.**

a) True

b) False

**Answer:** a

**Explanation:** The advantage of the block diagram is that it is possible to get the contribution of each block to the overall performance of the system.

**6. The overall transfer function from block diagram reduction for cascaded blocks is :**

a) Sum of individual gain

b) Product of individual gain

c) Difference of individual gain

d) Division of individual gain

**Answer:** b

**Explanation:** Gain of block get multiplied when they are cascaded where cascaded means that the blocks are in series combination with no summer in between.

**7. The overall transfer function of two blocks in parallel are :**

a) Sum of individual gain

b) Product of individual gain

c) Difference of individual gain

d) Division of individual gain

**Answer:** a

**Explanation:** The gains get added as the blocks are connected in parallel with the summer in between and they are connected with the same sign.

**8. Transfer function of the system is defined as the ratio of Laplace output to Laplace input considering initial conditions________**

a) 1

b) 2

c) 0

d) infinite

**Answer:** c

**Explanation:** By definition transfer function is the ratio of the laplace output to the input but the initial conditions mainly the stored energy is zero.

**9. In the following block diagram, G1=10/s G2=10/s+1 H1=s+3, H2=1. The overall transfer function is given by :**

a) 10/11s2+31s+10

b) 100/11s2+31s+100

c) 100/11s2+31s+10

d) 100/11s2+31s

**Answer:** b

**Explanation:** C/R=G2G1/1+G2H2+G1G2H2

C/R=100/11s2+31s+100.

**10. Oscillations in output response is due to :**

a) Positive feedback

b) Negative feedback

c) No feedback

d) None of the mentioned

**Answer:** a

**Explanation:** Oscillations are the unwanted sinuoidal signals with high gain in positive feedback and s the damping factor is absent in the positive feedback system entirely oscillations are present.