# Magnetically Coupled Circuits, Network Topology and Filters

 Question 1
The transfer function of a real system, $H(s)$, is given as:
$H(s)=\frac{As+B}{s^2+Cs+D}$
where A, B, C and D are positive constants. This system cannot operate as
 A low pass filter. B high pass filter C band pass filter. D an integrator.
GATE EE 2022   Electric Circuits
Question 1 Explanation:
Put $s=0, H(0)=\frac{A \times 0+B}{0+C \times 0+D}=\frac{B}{D}$
So, the system pass low frequency component. Put $s=\infty , H(\infty )=0$
For high pass filter, high frequency component should be non zero. Hence this system cannot be operated as high pass filter.
 Question 2
An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance M between the windings of the transformer is ____________ $\mu H$.(Round off to 2 decimal places.) A 12.14 B 68.26 C 51.1 D 78.4
GATE EE 2021   Electric Circuits
Question 2 Explanation: \begin{aligned} I_{1}&=\frac{5}{22}(p-p) \\ V_{0}&=j \omega M I_{1}=7.3=\left(2 \pi \times 10 \times 10^{3}\right) \times M \times\left(\frac{5}{22}\right) \\ M&=51.10 \mu \mathrm{H} \end{aligned}

 Question 3
The input impedance, $Z_{in}\left ( s \right )$ for the network shown is A $\frac{23s^{2}+46s+20}{4s+5}$ B $6s+4$ C $7s+4$ D $\frac{25s^{2}+46s+20}{4s+5}$
GATE EE 2021   Electric Circuits
Question 3 Explanation:
Circuit in s-domain, \begin{aligned} -S I_{1}+(4 s+5) I_{2} &=0 \\ \Rightarrow\qquad \qquad I_{2} &=\frac{s}{4 s+5} I_{1} \\ V_{1} &=(4+6 s) I_{1}-\frac{s^{2}}{4 s+5} I_{1} \\ \frac{V_{1}}{I_{1}} &=\frac{(4+6 s)(4 s+5)-s^{2}}{4 s+5} \\ &=\frac{24 s^{2}+30 s+16 s+20-s^{2}}{4 s+5} \\ Z_{\text {in }} &=\frac{23 s^{2}+46 s+20}{4 s+5} \end{aligned}
 Question 4
The line currents of a three-phase four wire system are square waves with amplitude of 100 A. These three currents are phase shifted by 120$^{\circ}$ with respect to each other. The rms value of neutral current is
 A 0 A B $\frac{100}{\sqrt{3}}$ A C 100 A D 300 A
GATE EE 2019   Electric Circuits
Question 4 Explanation: $I_N=I_a+I_b+I_c$
$(I_N)_{rms}=100A$
 Question 5
The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is
 A 11 B 12 C 13 D 14
GATE EE 2018   Electric Circuits
Question 5 Explanation:
Loops =b-(N-1)
5=b-(8-1)
b=12

There are 5 questions to complete.