Electrical Engg (EEE) - MCQ Practice Questions

An electrostatic voltmeter operates on the principle of electrostatic attraction between charged plates. Its input impedance is extremely high (essentially capacitive only), so it draws negligible current from the high-voltage source. This eliminates loading errors, which is critical when measuring high voltages where even small currents can disturb the source. It cannot practically measure up to 1 MV directly and is less sensitive at low voltages.

The divider ratio is $n=(R_1+R_2)/R_2=(9000+1000)/1000=10$. The actual high voltage is $V_{\text{HV}}=n\times V_{\text{out}}=10\times 10\text{kV}=100\text{kV}$. This principle of resistive voltage division is fundamental in high voltage measurement systems.

Townsend's second ionization coefficient $\gamma$ represents the number of secondary electrons emitted from the cathode surface per positive ion (or photon/metastable) bombarding it. Townsend's first coefficient $\alpha$ gives the number of ionizing collisions per unit path length by one electron. Together, $\alpha$ and $\gamma$ determine the condition for self-sustained discharge: $\gamma (e^{\alpha d}-1)=1$.

Sphere gaps are used as a standard measuring device in high voltage laboratories because the electric field between two equal spheres is nearly uniform (for small gap-to-diameter ratios), and the sparkover voltage is a well-defined, reproducible value that depends on sphere diameter and gap spacing. Standard tables (IEC 60052) provide sparkover voltages for different sphere sizes and gaps under specified atmospheric conditions, allowing accurate voltage measurement.

This is the standard definition of dielectric strength — the electric field intensity at which breakdown occurs.

For a coaxial cylindrical geometry, the electric field varies as $E(r)=\frac{V}{r\ln (r_2/r_1)}$. The maximum field occurs at $r=r_1$ (inner conductor surface):

Numerically, $\ln (4/1)=\ln 4\approx 1.386$, so the field is highest at the inner conductor.

To minimize $E_{\max }=\frac{V}{r_1\ln (r_2/r_1)}$ for fixed $V$ and $r_2$, we differentiate with respect to $r_1$ and set to zero. This yields the condition $\ln (r_2/r_1)=1$, i.e.,

This is the well-known optimum ratio for coaxial cable insulation design.

By definition of the standard impulse waveform $1.2/50\mu \text{s}$: the front time is $1.2\mu \text{s}$ (time to peak) and the tail time is $50\mu \text{s}$, which is the time from virtual origin to the point where the voltage decays to

The $50\mu \text{s}$ parameter is specifically defined as the time to half the peak value on the tail.

The Streamer (Kanal) criterion states that an electron avalanche transforms into a streamer when the number of ion pairs in the avalanche head reaches a critical value of approximately $10^8$. This requires:

Option C describes the Townsend (self-sustaining discharge) criterion, not the Streamer criterion.

Grading rings (also called corona rings or stress control rings) are metallic toroidal rings fitted at the high-voltage ends of insulators and bushings. Their primary function is to redistribute the non-uniform electric field along the insulator surface, reducing the peak electric stress concentration at the metal-insulator junction. This prevents premature corona inception and surface flashover. They do not primarily serve a mechanical, grounding, or leakage-distance function.

For healthy, high-quality cable insulation (such as XLPE or impregnated paper), the dissipation factor $\tan \delta$ is very small, typically in the range:

Values significantly higher than this indicate moisture ingress, aging, or contamination. A $\tan \delta$ approaching $0.1$ or higher would indicate severely deteriorated insulation.

The apparent charge is the charge that, if injected at the terminals of the test object, would give the same reading on the measuring instrument as the actual partial discharge.

Back-flashover is a specific phenomenon where lightning strikes the tower top or shield (ground) wire. The large lightning current $I$ flowing through the tower footing resistance $R_f$ raises the tower potential to $V_{\text{tower}}=I\cdot R_f$. If this potential exceeds the insulator string's impulse flashover voltage, a flashover occurs from the grounded tower structure back to the (relatively lower potential) line conductor — hence the term 'back-flashover'. This is distinct from a shielding failure (direct stroke to conductor) and is strongly influenced by the tower footing resistance.

The back EMF is given by:

Substituting the values:

The air-gap flux in an induction motor is proportional to $V/f$. By keeping the V/f ratio constant as frequency is varied, the magnetic flux in the air gap remains constant, which ensures the motor can develop rated torque throughout the speed range without magnetic saturation or under-excitation. This is the fundamental principle of scalar (V/f) control.

The back EMF is:

The developed mechanical power is:

From the equivalent circuit of an induction motor, differentiating the torque expression with respect to slip and setting it to zero gives the slip at maximum torque:

This shows that increasing rotor resistance (e.g., by external resistance in wound-rotor motors) increases $s_m$, shifting the maximum torque to a higher slip value, which is the principle of rotor resistance speed control.

The speed of a DC motor is given by $N\propto \frac{V_a-I_a{R}_a}{\varphi }$. Reducing the armature voltage $V_a$ below the rated value reduces the back EMF and hence the speed — this gives speeds below base speed at constant torque. Field weakening (reducing $\varphi$) gives speeds above base speed at constant power. Hence armature voltage control is used for sub-base speed operation.

During regenerative braking, the kinetic energy of the load drives the motor above synchronous/no-load speed, causing the back EMF $E_b$ to exceed the supply voltage $V_a$. The machine then acts as a generator, and the current reverses direction, feeding electrical energy back into the DC supply. This is energy-efficient braking, unlike dynamic braking which dissipates energy as heat in resistors.