### Circuit & Field Theory - MCQs from AMIE exams (Summer 2018)

1. A voltage waveform V (t) =12t² is applied across a 1 H inductor for t ≥ 0, with the initial electric current through it is zero. The electric current through inductor for t ≥ 0 is given by

(a) 12t

(b) 24t

(c) 12t²

(d) 4t³

2. In the network shown, what is the electric current I in the direction shown

(a) 0 A

(b) (1/3) A

(c) (5/6) A

(d) 4 A

3. Which of the following cannot be connected in scries unless they are identical?

(a) Voltage source

(b) Current source

(c) Both

(d) Resistance

4. A system with transfer function G(s) = [(s² + 9)(s + 2)]/[(s + 1)(s + 3)(s + 4)] is exited by sinωt. The steady state output of the system is zero at

(a) Q = 1 rad/sec .

(d) Q = 2 rad/sec

(c) Q = 3 rad/sec

(d) Q = 4 rad/sec

5. For static magnetic field Maxwell’s curl equation is given by

(a) ∇.B̅ = μ

_{0}.J̅(b) ∇.B̅ = 0

(c) ∇xB̅ = μ

_{0}.J̅(d) ∇xB̅ = μ

_{0/}J̅6. Which of the following laws of electromagnetic theory is associated with force experienced by two loops of a wire carrying currents?

(a) Maxwell’s law

(b) Coulomb’ law

(c) Ampere’s law

(d) Laplace’s law

7. The electric flux and field intensity inside a conducting sphere is

(a) Minimum

(b) Maximum

(c) Uniform

(d) Zero

8. The gradient of xi + yj + zk is

(a) 0

(b) 1

(c) 2

(d) 3

9. The Ultimate result of the divergence theorem evaluates which one of the following

(a) Field intensity

(b) Field density

(c) Potential

(d) Charge and flux

10. The Gaussian surface is

(a) Real boundary

(b) Imaginary surface

(c) Tangential

(d) Normal

**Answers**

- (d) I = ∫(V(t)/L)dt = ∫12t
^{2}dt = 4t^{3} - (a) V
_{B}= 10 V. Apply KCL at node A gives V_{A}= 10 V ⇒ I = 0 - (b) Current sources can not be connected in series unless identical because in series all individual current sources have same values.
- (c) x(s) = ω/(s
^{2}+ ω^{2}); If s^{2}+ ω^{2 = }s^{2}+ 9 then ω^{2}= 9 ⇒ ω = 3 rad/sec - (b)
- (c)
- (d) According to Gauss law, the electric field inside a conducting sphere is always zero irrespective of how much charge resides on its surface. Due to zero electric field inside a sphere, the electric flux inside a sphere is zero.
- (d) Grad (xi + yj + zk) = 1 + 1 + 1 = 3. In other words, the gradient of any position vector is 3.
- (d) Gauss law states that the electric flux passing through any closed surface is equal to the total charge enclosed by the surface. Thus, it is given by, ψ = ∫∫ D.ds= Q, where the divergence theorem computes the charge and flux, which are both the same.
- (b) It is any physical or imaginary closed surface around a charge which satisfies the following condition: D is everywhere either normal or tangential to the surface so that D.ds becomes either Dds or 0 respectively.

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