# GATE EE 2005

 Question 1
In the figure given below the value of R is
 A 2.5$\Omega$ B 5.0$\Omega$ C 7.5$\Omega$ D 10.0$\Omega$
Electric Circuits   Basics
Question 1 Explanation:
The resultant (R) when viewed from voltage source $=\frac{100}{8}=12.5$
$R+10||10=12.5\Omega$
$\therefore \;\; R=12.5-10||10 =12.5-5=7.5\Omega$
 Question 2
The RMS value of the voltage u(t)= 3 + 4 cos (3t) is
 A $\sqrt{17}$ V B 5V C 7V D (3+2$\sqrt{2}$)V
Electric Circuits   Steady State AC Analysis
Question 2 Explanation:
R.M.S. value of d.c voltage $=V_{dc}^{(rms)}=3V$
R.M.S. value of a.c. voltage $=V_{ac}^{(rms)}=\left ( \frac{4}{\sqrt{2}} \right ) V$
Therefore, R.M.S. value of the voltage
$\sqrt{3^2+\left ( \frac{4}{\sqrt{2}} \right )^2}$
$=\sqrt{9+8}=\sqrt{17}V$

 Question 3
For the two port network shown in the figure, the Z-matrix is given by
 A $\begin{bmatrix} Z_{1} &Z_{1}+Z_{2} \\ Z_{1}+Z_{2} & Z_{2} \end{bmatrix}$ B $\begin{bmatrix} Z_{1} &Z_{1} \\ Z_{1}+Z_{2} & Z_{2} \end{bmatrix}$ C $\begin{bmatrix} Z_{1} &Z_{2} \\ Z_{2} & Z_{1}+Z_{2} \end{bmatrix}$ D $\begin{bmatrix} Z_{1} &Z_{1} \\ Z_{1} & Z_{1}+Z_{2} \end{bmatrix}$
Electric Circuits   Two Port Network and Network Functions
Question 3 Explanation:

$v_1=(i_1+i_2)Z_1 =Z_1i_1+Z_1i_2$
$v_2=Z_2i_1+Z_1(i_1+i_2) =Z_1i_1+(Z_1+Z_2)i_2$
From above, we can write,
$\text{Z-matrix}=\begin{bmatrix} Z_1 &Z_1 \\ Z_1 & Z_1+Z_2 \end{bmatrix}$
 Question 4
In the figure given, the initial capacitor voltage is zero. The switch is closed at t = 0. The final steady-state voltage across the capacitor is
 A 20V B 10V C 5V D 0V
Electric Circuits   Transients and Steady State Response
Question 4 Explanation:
At $(t\rightarrow 0^+)$. The capacitor act as short-circuit. At $(t\rightarrow \infty )$, the capacitor will become open circuit.

Therefore, voltage across capacitor $=\frac{20}{10+10}\times 10=10V$
 Question 5
If $\vec{E}$ is the electric intensity, $\triangledown \cdot (\triangledown \times \vec{E})$ is equal to
 A $\vec{E}$ B |$\vec{E}$| C null vector D Zero
Electromagnetic Fields   Coordinate Systems and Vector Calculus
Question 5 Explanation:
Divergence of a curl field is always zero.
i.e. $\triangledown \cdot (\triangledown \times \vec{E})=0$

There are 5 questions to complete.