# Topic: Electric Circuits (Test 3)

Topic: Electric Circuits
Q.1
The r.m.s value of the current i(t) in the circuit shown below is

A. 1/2 A
B.
C. 1 A
D.
Explaination / Solution:

Workspace
Report
Q.2
A function 1 – x2 + xis defined in the closed interval [-1, 1]. The value of x , in the open interval (-1, 1) for which the mean value theorem is satisfied, is
A. -1/2
B. -1/3
C. 1/3
D. 1/2
Explaination / Solution:

Lagrange’s mean value theorem states that if a function f(x) is continuous in close interval [a, b] and differentiable in open interval (a + b), then for point c in the interval, we may define

Since, polynomial function is always continuous and differentiable, so

Workspace
Report
Q.3
A three – bus network is shown in the figure below indicating the p.u. impedances of each element.

The bus admittance matrix, Y – bus, of the network is
A.
B.
C.
D.
Explaination / Solution:

Workspace
Report
Q.4
In the following graph, the number of trees (P) and the number of cut-set (Q) are

A. P = 2,Q = 2
B. P = 2,Q = 6
C. P = 4,Q = 6
D. P = 4,Q = 10
Explaination / Solution:

Workspace
Report
Q.5
The Thevenin equivalent impedance Zth between the nodes P and Q in the following circuit is

A. 1
B. 1 +S+ 1/S
C. 2+S+1/S
D.
Explaination / Solution:

Killing all current source and voltage sources we have,

Workspace
Report
Q.6
The graph associated with an electrical network has 7 branches and 5 nodes. The number of independent KCL equations and the number of independent KVL equations, respectively, are
A. 2 and 5
B. 5 and 2
C. 3 and 4
D. 4 and 3
Explaination / Solution:

Workspace
Report
Q.7
With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:
(i) 1Ω connected at port B draws a current of 3 A
(ii) 2.5Ω W connected at port B draws a current of 2 A

For the same network, with 6 V dc connected at port A, 1Ω connected at port B draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is
A. 6 V
B. 7 V
C. 8 V
D. 9V
Explaination / Solution:
No Explaination.

Workspace
Report
Q.8
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
A. k2
D.
Explaination / Solution:

In the equivalent star connection, the resistance can be given as

Workspace
Report
Q.9
The following series RLC circuit with zero conditions is excited by a unit impulse functions 𝛿(t).

For t > 0, the voltage across the resistor is
A.
B.
C.
D.
Explaination / Solution:

Workspace
Report
Q.10
In the following transistor circuit,  , and 𝛽 and all the capacitances are very large

The value of DC current IE is
A. 1 mA
B. 2 mA
C. 5 mA
D. 10 mA