NMRC JE ELECTRICAL SOLVED PAPER 2017

Consider an RLC series circuit

Since the current flowing through the circuit is common to all three circuit elements we can use this as the reference vector.

In the case of the resistor, both voltage and current are in the same phase. So the voltage phasor, V_R is in phase with I.

As we know that in the inductor, voltage leads current by 90° hence V_l is perpendicular to the current phasor in the leading direction.

In the case of the capacitor, the voltage lags behind the current by 90° so Vc is perpendicular to the current phasor in a downwards direction.

The resultant diagram, draw V_c in upwards direction. Now  V_s which is the vector sum of voltage V_r and V_L – V_C

Note:- The voltage Diagram and Impedance Diagram yield the same information

Using Pythagoras’s theorem on this voltage triangle to mathematically obtain the value of V_S as shown.

${V_s} = \sqrt {{V^2}_R + {{\left( {{V_L} – {V_C}} \right)}^2}}$

Since V_R = I_R; V_L = IX_L; Vc = IX_c

$\begin{array}{l}{V_s} = \sqrt {{{\left( {IR} \right)}^2} + {{\left( {I{X_L} – I{X_C}} \right)}^2}} \\\\{V_s} = I\sqrt {{{\left( R \right)}^2} + {{\left( {{X_L} – {X_C}} \right)}^2}} \\\\Z = \dfrac{{{V_s}}}{I}\\\\Z = \sqrt {{{\left( R \right)}^2} + {{\left( {{X_L} – {X_C}} \right)}^2}} \end{array}$

All the resistances are the same. Hence it is the condition of a balance wheat stone bridge so no current will flow from 1Ω vertical resistance, so it can be imagined that it is opened. Then the equivalent resistance between A and B is
R_eq = (1+1) || (1+1) || 1 Ω
R_eq = 2 || 2 || 1 Ω
R_eq = 0.5 Ω

During Mutual Inductance between two coils, we assume that the flux produced by one coil is entirely linked with the other coil. But practically it is not true, the certain portion of the flux of one coil does not link with the other coil.

The ratio of the portion of the flux of one coil link with the other coil to the entire flux produced by the coil is referred as the coefficient of magnetic coupling.

or

The coupling coefficient K is the degree or fraction of magnetic coupling that occurs between the circuit.

K =M/√L₁L₂

In this circuit configuration of a transistor, the base terminal is used as a common terminal between input and output as depicted in Fig. The input signal is applied between the emitter and base terminals. The output will be taken from the collects and base terminals. To explain the operation of NPN and PNP transistors, the common base configuration is used.

Characteristic of common base (CB)

There are two important characteristics of CE

(1) input characteristics.

(2) Output characteristics.

Input Characteristic. It is the curve between base current IB and emitter-base voltage V_BE at constant collector-base voltage V_CB.

The emitter current I_E increases rapidly with a small increase in emitter-baa voltage V_EB which means that input resistance is very small.

In fact, the input resistance is the opposition offered to the signal current. As a very small V_EB is sufficient to produce a large flow of emitter current, therefore, the input resistance is quite small, of the order of a few ohms.

Output Characteristic. It is the curve between collector current Ic and collector-base voltage V_CB at constant emitter current I_E. A very large change in collector-base voltage produces only a tiny change in collector current. This means that output resistance is very high.

Norton equivalent resistance for the given network is

R = (R₁ || R₂) + R₃

R = (2 || 6) + 3 = (2 x 6)(2 + 6) + 3 = 4.5Ω

Dielectric heating (also called High-frequency capacitive heating) is employed for heating insulators like wood, plastics, ceramics etc.

• In dielectric heating, the current is drawn by the capacitor. When an AC supply voltage is applied across the capacitor plates, the current does lead the supply voltage by exactly 90° and there is always an in-phase component of the current. Since the dielectric heating is involved in the capacitor, the power factor will be leading in the case of dielectric heating. The value of the power factor for a particular non-conducting material is constant.

• Damper windings are windings that are wound to the rotor poles of the machine (winding is similar to that of an induction machine) which help in two ways.
• We all know that a synchronous machine is not self-starting. Thus providing damper windings help synchronous machines to act as an induction motor ( only at starting). Which helps the machine to self-start.

The Q factor of a coil can be measured by measuring accurately the inductance and effective resistance of the coil for a specific signal. The inductance of an inductive coil is generally measured by the usual inductive circuit like Maxwell-Wein Bridge, Hay Bridge, Anderson’s bridge, etc.

The Anderson’s bridge gives an accurate measurement of the self-inductance of the circuit. The bridge is the advanced form of Maxwell’s inductance capacitance bridge. Anderson bridge is used to measure inductance values over a wide range while only requiring a fixed capacitance of a moderate value. A schematic diagram of the Anderson bridge is shown below. The resistors are chosen such that R₁R₃ = R₂R₄. Adjustments of R₅ are used to balance the circuit. At balance, the inductance is given by

L=C[R₁R₃+(R₃+R4)R₅].

This method is capable of precise measurement of inductance and a wide range of values from a few μH to several Henery.

There are two type of losses in a transformer;

1. Copper Losses
2. Iron Losses or Core Losses or Insulation Losses

Copper losses ( I²R) are variable losses that depend on Current passing through transformer windings while Iron Losses Core Losses or Insulation Losses depend on Voltage.

As seen the copper loss of the alternator are dependent upon current and iron loss on voltage. Hence the total loss of the alternator depends on VOLT-AMPERE. These losses are independent of load power factor. That is why the rating of the transformer is in kVA

The instantaneous value of alternating current is given as

V = Vmax sinωt

V = 200 sin314t.

Vmax = 200V

RMS Value = V_max/√2 = 200/√2 = 141.4 V