JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II NETWORK ANALYSIS AND TRANSMISSION LINES Previous Question Paper (October - 2020 - R18)
Answer any five questions. All questions carry equal marks.
Main
Derive an expression for coefficient of coupling between two mutually coupled coils.
Answer
Consider two coils with self-inductances L1 and L2 placed in proximity such that they are magnetically coupled. Let M be the mutual inductance between them. The flux produced by coil 1 is divided into two parts: the leakage flux (Φl1) and the useful flux that links coil 2 (Φm1). Similarly, for coil 2, the flux is divided into leakage flux (Φl2) and the flux linking coil 1 (Φm2).
The self-inductances are defined as:
The mutual inductance is defined by the flux linkage of one coil due to current in the other:
Multiplying the two expressions for M:
Since Φm1 = k1Φ1 and Φm2 = k2Φ2, where k1 and k2 are the fractions of flux linking the other coil:
Defining the coefficient of coupling as K = √(k1k2), we obtain:
The number of turns in two coupled coils is 250 and 750 respectively. When 2.5 A current flows in coil 1, the total flux in this coil is 0.3 milli Wb and the flux linking the second coil is 0.15 Wb. Determine L1, L2, M and K.
Answer
Given: N1 = 250, N2 = 750, I1 = 2.5 A, Φ1 = 0.3 mWb = 0.3 × 10-3 Wb, Φm1 = 0.15 mWb = 0.15 × 10-3 Wb.
- L1 Calculation:L1 = (N1 × Φ1) / I1 = (250 × 0.3 × 10-3) / 2.5 = 0.03 H = 30 mH
- M Calculation:M = (N2 × Φm1) / I1 = (750 × 0.15 × 10-3) / 2.5 = 0.045 H = 45 mH
- K Calculation:K = Φm1 / Φ1 = 0.15 / 0.3 = 0.5
- L2 Calculation: Using M = K√(L1L2):L2 = M2 / (K2 × L1) = (0.045)2 / (0.52 × 0.03) = 0.27 H = 270 mH
Explain the following: (i) sub graph (ii) connected graph and (iii) Planar graph.
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Obtain the fundamental circuit matrix for the graph in the figure 1. Choose the tree consisting of branches 6, 7, 8 and 9.
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Obtain the response of the current flowing through a Series RLC circuit when excited by a step voltage by closing the switch at t = 0+.
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The circuit in figure 2 is operating under steady state condition when the switch is at position ‘a’ and at t = 0, the switch is moved to position ‘b’. Determine the current i(t).
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An inductance of 0.6 H, a resistance of 6 ohm and a capacitance of 10 μF are in series across a 230 V, A.C supply. Calculate the frequency at which the circuit resonates. Find the current at resonance, bandwidth, half power frequencies and the voltage across capacitance at resonance.
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Determine the driving point impedance V1/I1, transfer impedance V2/I1 and voltage transfer ratio V2/V1 for the network shown in Figure 3.
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The z-parameters of a certain two port network are Z11 = 5 Ω, Z12 = Z21 = 3 Ω and Z22 = 4 Ω. Determine its y-parameters, transmission parameters, and hybrid parameters (h) and inverse hybrid parameters (g).
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Calculate the characteristic impedance for the following line parameters: R = 10.4 ohms/km; L = 0.00367 H/km; C = 0.00835 μF/km and G = 10.8×10-6 mhos/km.
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State the properties of infinite line.
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Derive an expression for the input impedance of distortion less lines. Deduce the input impedance of open and short circuited distortion less lines.
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