GTU BE01000051 Basic Electrical Engineering Summer 2026 Solved Paper & Solutions

Kirchhoff's Current Law (KCL) states that the algebraic sum of the currents meeting at a node (junction) is zero. In other words, the total current entering a node equals the total current leaving it.

Demonstration: at a node, 5 A and 3 A flow in, and two branches carry the current out.

Current in = $5 + 3 = 8$ A. Current out = $6 + 2 = 8$ A. They are equal, so KCL holds. KCL is based on the conservation of charge: no charge is stored at a node.

Let $V$ be the rms voltage, $I$ the rms current and $\phi$ the phase angle between them.

• Active (true) power $P$: the power that does useful work and is used up by the load. $P = VI\cos\phi$, unit watt (W).
• Reactive power $Q$: the power that moves back and forth between the source and the inductor or capacitor, and does no useful work. $Q = VI\sin\phi$, unit volt-ampere reactive (VAR).
• Apparent power $S$: the product of the rms voltage and current. $S = VI$, unit volt-ampere (VA).
• Power factor: the ratio of active power to apparent power. $\text{pf} = \dfrac{P}{S} = \cos\phi$.

The three powers are related by $S^2 = P^2 + Q^2$. The power factor is lagging for an inductive load and leading for a capacitive load, and its value is between 0 and 1.

Thevenin's theorem: any linear network, seen from two terminals, can be replaced by a voltage source $V_{th}$ in series with a resistance $R_{th}$.

From the figure: $V_1 = 10$ V, $R_1 = 8\ \Omega$, $R_2 = 2\ \Omega$, $V_2 = 20$ V, $R_L = 1.4\ \Omega$.

The voltage across the open terminals is

Check: $V_2 - I R_2 = 20 - 2 = 18$ V.

The two-wattmeter method measures the power of a three-phase, three-wire load with two wattmeters.

CC is the current coil and PC is the pressure (voltage) coil. The current coils are in two lines, and the pressure coils go from each of those lines to the third line.

For a balanced load with phase angle $\phi$ and line values $V_L$, $I_L$:

Here $\phi$ is the angle between the phase voltage and the phase current of the load. The readings change with the power factor of the load, so the power factor can also be found from the two readings. It comes from $\tan\phi = \sqrt{3}\,\dfrac{W_1 - W_2}{W_1 + W_2}$. The two wattmeters need not have the same reading. At unity power factor, $W_1 = W_2$. At power factor 0.5, one wattmeter reads zero. Below 0.5, one reads negative.

In a series RLC circuit, resonance occurs when the inductive reactance equals the capacitive reactance, $X_L = X_C$. The two voltages $V_L$ and $V_C$ are then equal and opposite, so they cancel. The circuit behaves as a pure resistance.

Condition and resonant frequency

At resonance:

• Impedance $Z = \sqrt{R^2 + (X_L - X_C)^2} = R$, the minimum value.
• Current $I = V/R$, the maximum value.
• Power factor $= \cos\phi = 1$, since the circuit is purely resistive.
• $V_L = V_C = I X_L$, and each can be much larger than the supply voltage. The ratio $Q = \omega_0 L / R$ is the quality factor.

Graphs against frequency

The current graph peaks at $f_0$. The impedance graph has its lowest point $R$ at $f_0$. $V_C$ peaks a little below $f_0$, and $V_L$ a little above it.

A single-phase transformer has two windings on a common laminated core.

Main parts

• Core: thin laminations of silicon steel, which give a low-reluctance path to the flux and reduce eddy current loss.
• Primary winding: connected to the supply.
• Secondary winding: connected to the load.
• Insulation, tank and bushings: large transformers are placed in an oil-filled tank, which cools them.

Split-phase induction motors have a main winding and an auxiliary (starting) winding, placed $90^\circ$ apart in space. A phase difference between their currents makes the starting torque.

Types

1. Resistance split-phase motor: the starting winding has a high resistance.
2. Capacitor-start motor: a capacitor in series with the starting winding, which is cut out by a centrifugal switch.
3. Capacitor-start capacitor-run (two-value capacitor) motor: one capacitor for starting and a smaller one stays in circuit during running.
4. Permanent-split capacitor (PSC) motor: one capacitor stays in circuit all the time.

Most suitable for heavy duty: the capacitor-start capacitor-run motor. The starting capacitor gives a high starting torque for a heavy load. The running capacitor keeps the power factor high and the running torque smooth, so the efficiency is good.

The B-H curve shows how the flux density $B$ of a magnetic material changes with the magnetic field intensity $H$.

Magnetisation curve

When an unmagnetised material is magnetised, $B$ rises with $H$ as follows.

• At the start, $B$ rises slowly, because the small magnetic domains of the material begin to turn. Then it rises almost in a straight line, when most domains turn towards the field.
• At the knee, the rise slows down.
• Beyond it the material is saturated, because all domains are lined up, and $B$ hardly increases. This limits the flux of a machine, so the knee is the working point of a transformer or a motor.

Hysteresis loop

If $H$ is reversed and varied through a full cycle, $B$ lags behind $H$. The curve is a closed loop.

• Retentivity $B_r$: the flux density that remains when $H = 0$.
• Coercivity $H_c$: the reverse field that is needed to bring $B$ to zero.
• The area of the loop is the energy lost per cycle in a unit volume of the material. It appears as heat and is called the hysteresis loss.

The loop is traced again and again when the field is alternating, and so the loss occurs in each cycle. A soft material, such as silicon steel, has a narrow loop and a small loss, and it is used in transformer cores. A hard material, such as steel, has a wide loop and is used for permanent magnets.

Types of lamps: incandescent (filament) lamp, halogen lamp, fluorescent tube, compact fluorescent lamp (CFL), LED lamp, and mercury or sodium vapour lamps for streets.

Most suitable for domestic use: the LED lamp.

• It uses much less power for the same light, so the electricity bill is lower.
• It has a very long life.
• It gives light at once, has no harmful mercury, and works at low heat.

A Miniature Circuit Breaker (MCB) is an automatic switch that opens the circuit when there is an overload or a short circuit. It can be switched on again after the fault is removed.

It has two tripping mechanisms:

• Thermal (overload) trip: a bimetallic strip is heated by the current. For a small overload, it bends slowly after some time and releases the latch.
• Magnetic (short-circuit) trip: a solenoid carries the current. In a short circuit, the large current pulls the plunger at once, and this trips the contacts.

When the contacts open, the arc is drawn into an arc chute, where it is cooled and stopped. The handle goes to the OFF position, and the MCB is reset by hand.

A BLDC (Brushless DC) motor is a DC motor in which the brushes and the commutator are replaced by an electronic circuit.

Construction: the stator carries a three-phase winding. The rotor has permanent magnets. Hall sensors inside the motor sense the position of the rotor poles. An electronic controller (inverter) supplies the stator.

Working

1. The Hall sensors tell the controller which rotor pole is near which stator coil.
2. The controller switches the DC supply to the stator coils in a fixed order. This is electronic commutation.
3. The stator coils set up a magnetic field that moves around the stator.
4. The permanent magnets of the rotor follow this field, so the rotor turns.
5. The speed is controlled by changing the voltage with PWM (pulse width modulation), and the direction by changing the order of switching.
6. The torque stays smooth because the controller always keeps the stator field ahead of the rotor.

There are no brushes to wear, so the motor is quiet, efficient and has a long life. Its main uses are in fans, drones, electric vehicles, hard disks and washing machines, since the speed is easy to control and the efficiency is high.

A lighting fixture (luminaire) is the complete unit that holds the lamp, connects it to the supply and protects it, and often controls the light. A reflector is a surface that sends the light of the lamp in the wanted direction, and so increases the light on the working area.

• Fixtures: a batten holder, a tube light fitting, a pendant light.
• Reflectors: a parabolic reflector in a torch or a vehicle headlight, a conical metal reflector on a street lamp.

A lighting scheme is the way the light of the lamps is spread over a room. The schemes are listed by how much light goes downwards and how much goes upwards.

The arrows show the direction of the light. Semi-direct and semi-indirect lighting lie between these three.

Earthing is the connection of the metal body of an electrical equipment to the general mass of the earth through a wire of low resistance.

Importance of earthing

• It protects persons from electric shock. A fault current flows into the earth and not through the body.
• It protects the equipment from damage by leakage and fault currents.
• It makes the fuse or the circuit breaker operate, because a large fault current flows.
• It gives a safe path to the earth for lightning and surge currents.

Types of earthing

1. Pipe earthing
2. Plate earthing
3. Rod earthing
4. Strip or wire earthing

Pipe earthing in detail

A galvanised iron (GI) pipe, about 40 mm in diameter and 2.5 m or more in length, is buried vertically in the ground. The lower part of the pipe has holes, which let moisture reach it. The pipe is surrounded by layers of charcoal and salt, which keep the soil wet and lower the resistance. The earth wire is bolted to the top of the pipe. A funnel on the top is used to pour water into it from time to time. The resistance of the earth connection should be low, and it is tested at regular intervals.