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Network Analysis - Research Paper Example

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This paper is focused on the analysis of the network. Namely, the solutions for different tasks are presented. The task can sound like that: the three components R, L, and C are placed first in series and then in parallel across a supply of angular frequency ω. Write expressions, in complex form, for the impedance of the series circuit.
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Download file to see previous pages A machine consumes a power of 10 kW and a reactive power of 4 kvar at a current of (6 + j4)A. Determine the applied voltage, expressing your answer in complex form. Solution: Here as given, Average Power, P = 10 kW, Reactive Power, Q = 4 kvar, Current I = (6+j4) A
Let S be the Apparent Power then we know that, Apparent Power S = Re{VI*} - Im{VI*} S = P - jQ, substituting the values of P & Q S = 10 10³ - j4 10³ S = (10 –j4) 10³ …. Eq.
Since S = VI*... Eq. 2(2) Where V is the applied voltage and I* is the conjugate of I. As we know that if z = a + jb is a complex number then z* = a – jb Therefore, I* = 6 - j4
Now equating Eq. 1(2) & 2(2) and substituting the value of I* we have, V (6 - j4) = (10 – j4) 10³ V = (10 – j4) 10³/ (6 - j4)
After rationalizing, V = (6 + j4)(10 – j4) 10³/ (6² + 4²) V = (76 + j16) 10³/ 52 V = (1.46 + j0.30) 10³
Network 5 Hence, V = 1.46 10 + j300 …. Eq. 3(2)Which is the applied voltage expressed in complex form. Solution: 3(a) Let is the applied voltage & be the resulting current
through the given circuit then for complex impedance circuit is given as, = Expj …. Eq. 1(a3) Where . Let be the phase difference between voltage and current than current = Expj( + …. Eq. 2(a3) Since impedance in time domain is defined as, = …. Eq. 3(a3) From equations 1(a) & 2(a) we have, = as R=1 (given) =
Or in polar form, …. Eq. 4(a3) Multiplying by 1 /to yield effective value we have, Z= or Z= 0.707…. Eq. 5(a3)
Equation 5(a). is the required impedance in polar form. admittance is the reciprocal of impedance so, if Y is admittance then Y = 1/Z…. Eq.1(b3)...
admittance Y=1/Z, or, Yeq=1/Zeq

1/Zeq=Yeq From Eq. 1(b1)

Hence, Yeq=1/R+j(C -1/L) . Eq. 2(b1)

Equation 2(b) gives the expression of admittance for RLC parallel circuit impedance.







Network 4

2. A machine consumes a power of 10 kW and a reactive power of 4 kvar at a

current of (6 + j4)A. Determine the applied voltage, expressing your answer in complex

form.

Solution: Here as given,

Average Power, P = 10 kW,

Reactive Power, Q = 4 kvar,

Current I = (6+j4) A

Let S be the Apparent Power then we know that,

Apparent Power S = Re{VI*} - Im{VI*}

S = P - jQ, substituting the values of P & Q

S = 1010 - j410

S = (10 -j4) 10 . Eq. 1(2)

Since S = VI* . Eq. 2(2)

Where V is the applied voltage and I* is the conjugate of I.

As we know that if z = a + jb is a complex number then

z* = a - jb

Therefore, I* = 6 - j4

Now equating Eq. 1(2) & 2(2) and substituting the value of I* we have,

V (6 - j4) = (10 - j4) 10

V = (10 - j4) 10/ (6 - j4)

After rationalizing, V = (6 + j4)(10 - j4) 10/ (6 + 4)

V = (76 + j16) 10/ 52

V = (1.46 + j0.30) 10
Network 5

Hence, V = 1.4610 + j300 . Eq. 3(2)

Which is the applied voltage expressed in complex form.

Solution: 3(a) Let is the applied voltage & be the resulting current

through the given circuit then for complex impedance circuit is given as,

= Expj . Eq. 1(a3)

Where. Let be the phase difference between voltage and current then ...Download file to see next pagesRead More
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