# EC GATE 2009 - Online Test

Q1. Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y - z plane and parallel to the y axis. The other wire is in the x - y plane and parallel to the x - axis. Which components of the resultingmagnetic field are non-zero at the origin ?

Explaination / Solution:

Due to 1 A current wire in x - y plane, magnetic field be at origin will be in x direction.
Due to 1 A current wire in y - z plane, magnetic field be at origin will be in z direction.
Thus x and z component is non-zero at origin.

Q2. A fully charged mobile phone with a 12 V battery is good for a 10 minute talktime. Assume that, during the talk-time the battery delivers a constant current of 2 A and its voltage drops linearly from 12 V to 10 V as shown in the figure. How much energy does the battery deliver during this talk-time?

Explaination / Solution:

The energy delivered in 10 minutes is

Q3. If a vector field is related to another vector field through which of the following is true? (Note : C and SC refer to any closed contour and any surface whose boundary is C . )
Explaination / Solution:

Hence (B) is correct option.

Q4. The full form of the abbreviations TTL and CMOS in reference to logic families are
Explaination / Solution:

TTL -> Transistor - Transistor logic CMOS -> Complementary Metal Oxide Semi-conductor

Q5.
In the following a stable multivibrator circuit, which properties of  V0(t) depend on R2?

Explaination / Solution:

The R2  decide only the frequency.

Q6. A magnetic field in air is measured to be What current distribution leads to this field ?
[Hint : The algebra is trivial in cylindrical coordinates.]

Explaination / Solution:

Q7. A white noise process X(t) with two-sided power spectral density 1 X 10-10  W/HZ is input to a filter whose magnitude squared response is shown below.

Explaination / Solution:
No Explaination.

Q8.
The ratio of the mobility to the diffusion coefficient in a semiconductor has the units
Explaination / Solution:

Q9. Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown ?

Explaination / Solution:

Rectangular and cylindrical waveguide doesn’t support TEM modes and have cut off frequency. Coaxial cable support TEM wave and doesn’t have cut off frequency.

Q10. In the circuit below, the diode is ideal. The voltage V is given by

Explaination / Solution:

Let diode be OFF. In this case 1 A current will flow in resistor and voltage across resistor will be V = 1.V
Diode is off, it must be in reverse biased, therefore
Vi- 1 > 0 " Vi > 1
Thus for Vi > 1 diode is off and V = 1V
Option (B) and (C) doesn’t satisfy this condition.
Let Vi < 1. In this case diode will be on and voltage across diode will be zero and
V = Vi
Thus V = min(Vi,1)