All Q&A

1

**Find the current in each branch of the network using Kirchhoff’s law**

**Fig.23**

Applying KVL in mesh I, II and II respectively
\(-2I_1-3I_2+{7I}_3=12\) … (1)

2

**A circuit receives 50 A current at a power factor of 0.8 lag from a 250, 50 Hz, 1-ph A.C. supply. Calculate the capacitance of the capacitor which is required to be connected across the circuit to make the power factor unity.**

From the given data, we have \(cos\ \theta=0.8\),
Or \(\theta=\cos^{-1}{0.8}={36.86}^0\)

3

**Explain **

**Star – delta conversion****Delta – star conversion with the help of a purely resistive circuit**

In this transformation any resistance in delta network can be found out if the resistances of corresponding star network are known.
Here the branch resistances in the star connections are

4

**Derive an expression for the resonant frequency of a parallel circuit, one branch consisting of a coil of inductance L and resistance R and the other branch of capacitance C.**

The series RL circuit with parallel C is given in Fig. 19. The designed circuit consists of resistance R, inductance L are in series with parallel configuration of capacitance C. Let us consider the current I flowing through the RLC circuit by the a.c. voltage source with constant value of V.

5

**The galvanometer shown in the circuit has a resistance of 5 Ω. Find the current through the galvanometer using Thevenin’s theorem.**

**Fig.22(a)**

Equivalent resistance of the circuit \(R_{th}=\frac{10\times15}{10+15}+\frac{12\times16}{12+16}=6+6.86=12.86\ \mathrm{\Omega}\)

6

**A two element series circuit consumes 700 V of power and has power factor of 0.707 leading when energized by a voltage source of waveform \(v=141\sin\left(314t+30^{\circ}\right)\). Find out the circuit element.**

The power dissipated by the coil is \(P_C=I_{rms}V_{rms}\ cos\ \phi\)
For this problem \(V_{rms}=\frac{V_{peak}}{\sqrt2}=\frac{141}{\sqrt2}=100\ V\)

7

**Derive the expression of quality factor of series R-L-C circuit at resonance.**

The quality factor is , in general, defined as the ratio of resonant frequency to bandwidth. It is given by

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