Q&A: practice questions with answers

Concept: Motional EMF $\epsilon =Blv\sin \theta$.

1. It depends on field $B$, length $l$, speed $v$ and the angle $\theta$ between $v$ and $B$.
2. Resistance of the conductor affects only the induced current ($I=\epsilon /R$), not the EMF itself.

Yaad rakhein: EMF is "cause", current is "effect" — $R$ changes the effect only.

Answer: (C) The resistance of the conductor

Concept: Lenz's law: the induced current opposes the change that produces it (energy conservation).

1. As the ring enters/moves through the field, flux through it changes and eddy/induced current flows.
2. The induced current experiences a magnetic force opposing the motion — a retarding force upward.
3. So the ring falls slower than free fall; it is not pushed up or made faster.

Yaad rakhein: Induction always "brakes" the motion (magnetic braking).

Answer: (B) It slows down as it falls.

Concept: A thermistor is a temperature-sensitive resistor; it may be NTC (resistance falls with temperature) or PTC (resistance rises).

1. Whether the coefficient is positive or negative is decided by the construction material (metal oxides etc.) and the temperature region.
2. The temperature change can come from self-heating by the current, or from the surroundings — which may heat or cool it.

Yaad rakhein: NTC for temperature sensing; PTC for self-resetting fuses/over-current protection.

Answer: (B) positive or negative temperature coefficients; heating or cooling

Concept: The barrier (knee) potential of a p-n junction depends on the semiconductor material.

1. Germanium: about $0.3\text{V}$ at ${25}^{\circ }\text{C}$; silicon: about $0.7\text{V}$.
2. Barrier potential decreases by roughly $2\text{mV}$ per ${}^{\circ }\text{C}$ rise in temperature.

Yaad rakhein: Ge = 0.3 V, Si = 0.7 V.

Answer: (A) 0.3 V

Concept: The MCS-51 (8051) family includes 8051, 8031 (ROM-less), 8751 (EPROM) and their CMOS versions 80C51BH, 80C31BH, 87C51.

1. 80C51BH, 80C31BH and 87C51 are standard 8051-series members.
2. 8044AH is Intel's RUPI-44 serial communication controller (8051 core with an SDLC/HDLC interface) — a separate product line, not listed as an 8051-series microcontroller.

Yaad rakhein: 8051 family numbers contain "51" or "31"; 8044 is the odd one.

Answer: (B) 8044AH

Concept: Lenz's law gives the direction of induced EMF/current: it opposes the change in magnetic flux that causes it.

1. This is a consequence of conservation of energy — the induced current must do work against the cause.
2. The direction depends on whether flux is increasing or decreasing, not on the amount of flux (option D wrong).

Yaad rakhein: The minus sign in $\epsilon =-\frac{d\varphi }{dt}$ is Lenz's law.

Answer: (A) The induced current always opposes the change in magnetic flux that produced it.

Concept: The forbidden energy gap $E_g$ between the valence band and the conduction band decides whether a material conducts.

1. Conductors: valence and conduction bands overlap – no forbidden gap, electrons flow freely.
2. Semiconductors (Si, Ge): narrow gap of about $1\text{eV}$, so a little energy (heat/light) lifts electrons into the conduction band.
3. Insulators: wide gap ($>5\text{eV}$), so electrons cannot cross at ordinary temperatures.

Yaad rakhein: Gap order – conductor $0$ < semiconductor $\approx 1\text{eV}$ < insulator $>5\text{eV}$.

Answer: (B) Conductors have no forbidden gap, semiconductors a narrow gap and insulators a wide gap.

Concept: A thermocouple works on the Seebeck effect – an emf is produced when its two junctions are at different temperatures.

1. Over its working range the emf is approximately proportional to the temperature difference: $E\approx \alpha (T_1-T_2)$, where $\alpha$ is the Seebeck coefficient.
2. Exactly, $E=a\theta +b{\theta }^2$ (slightly parabolic), but the second term is small, so the relation is treated as linear for measurement.

Yaad rakhein: Thermocouple → Seebeck effect → emf ∝ temperature difference (linear).

Answer: (D) linear

Concept: For a long solenoid the field inside is $B={\mu }_{0}nI$ ($n$ = turns per unit length) – it does not depend on the position inside.

1. The fields of the closely wound turns add up to give parallel, equally spaced field lines inside – a uniform field along the axis.
2. At the ends the field drops to about half ($\frac{1}{2}{\mu }_{0}nI$), and outside it is nearly zero – so options (A), (C), (D) are wrong.

Yaad rakhein: Long solenoid ≈ bar magnet with a uniform field inside, almost zero outside.

Answer: (B) uniform

Concept: Faraday's law: induced emf $e=-\frac{d\varphi }{dt}$ – it depends on the rate of change of flux, not on the flux itself.

1. Flux increases linearly: $\varphi =kt$.
2. $e=-\frac{d\varphi }{dt}=-k$ = a constant value.
3. It would be zero only if the flux did not change at all.

Trick: Flux ∝ $t$ ⇒ slope constant ⇒ emf constant.

Answer: (A) constant

Concept: Work-energy theorem: the work done by the net force equals the gain in kinetic energy, $K=F·x$.

1. Starting from rest, $v^2=u^2+2ax=2ax$.
2. $K=\frac{1}{2}m{v}^2=\frac{1}{2}m(2ax)=max$.
3. Since $m$ and $a$ are constant, $K\propto x$ – a straight-line (linear) relation.

Trick: Constant force ⇒ $K=Fx$ ⇒ $K\propto x$ (not $\sqrt{x}$ or $x^2$).

Answer: (C) $K\propto x$

Concept: SI has seven fundamental units (m, kg, s, A, K, mol, cd); any unit formed by combining them is a derived unit.

1. Volt $={\text{kg m}}^2{\text{s}}^{-3}{\text{A}}^{-1}$, Newton $={\text{kg m s}}^{-2}$, Joule $={\text{kg m}}^2{\text{s}}^{-2}$ – all derived.
2. Options (A), (B), (C) contain only fundamental units (metre, kilogram, ampere, kelvin, mole, second).

Yaad rakhein: Units named after scientists (volt, newton, joule, watt, pascal) are always derived.

Answer: (D) Volt, Newton, Joule

Concept: In this two-diode circuit each diode conducts only when the input exceeds its battery voltage; between the two thresholds both diodes stay off and no output appears.

1. For $V_i>+E_1$, $D_1$ conducts and output follows $V_i-E_1$; for $V_i<-E_2$, $D_2$ conducts.
2. For $-E_2<V_i<+E_1$ both diodes are reverse biased, so $V_o=0$ – the transfer curve is flat.
3. This flat band where the input produces no output is called the dead zone (dead band).

Yaad rakhein: Input present but output zero = dead zone; cut-off and saturation are transistor regions, not diode-clipper terms.

Answer: (D) dead zone

Concept: An electrostatic voltmeter measures voltage by the force between charged plates. Its range is extended by a potential divider, not by a series resistor as in ordinary voltmeters.

1. With a resistance potential divider the instrument reads only a known fraction of the total voltage (used for DC and low-frequency AC); for pure AC a capacitance divider is also used.
2. A plain resistor or capacitor in series cannot give a fixed multiplying factor for an instrument that draws almost no current, so options (B) and (D) are wrong.

Yaad rakhein: Electrostatic voltmeter range ↑ → potential divider (resistance / capacitance).

Answer: (A) Resistance Potential Divider

Concept: A piezoelectric crystal (quartz, Rochelle salt) produces charge only while the applied force is changing; under a steady force the charge leaks away through the crystal and amplifier resistance.

1. Hence it responds to dynamic (varying) displacement, vibration, shock and pressure, but cannot hold a reading for a static displacement.
2. Its high natural frequency makes it ideal for vibration and accelerometer applications.

Yaad rakhein: Piezo = dynamic only; for static displacement use LVDT or strain gauge.

Answer: (B) Piezoelectric transducer can be used for the measurement of dynamic displacement only.

Concept: Power is the rate of doing work: $P=\frac{W}{t}$, so for fixed work $t=\frac{W}{P}$, i.e. $t\propto \frac{1}{P}$.

1. Original: $t=\frac{W}{P}$.
2. New power $2P$: $t^{\prime }=\frac{W}{2P}=\frac{t}{2}$.

Trick: Double the power → half the time (inverse relation).

Answer: (A) $\frac{t}{2}$

Concept: Resistivity $\rho$ is a property of the material; resistance $R=\rho \frac{l}{A}$ depends on dimensions.

1. $\rho$ depends on the material and its atomic structure (free-electron density) and on temperature.
2. Length and area change $R$, not $\rho$ – a long and a short copper wire have the same resistivity.

Yaad rakhein: Resistance → size matters; resistivity → only material and temperature.

Answer: (C) Length of the conductor

Concept: In free fall, total mechanical energy is conserved: loss in PE = gain in KE.

1. Initial PE $=mgh$; at half height PE $=mg\frac{h}{2}=\frac{1}{2}mgh$.
2. KE gained $=mgh-\frac{1}{2}mgh=\frac{1}{2}mgh$, i.e. $\frac{1}{2}$ of the initial PE.

Trick: PE ∝ height, so fraction of PE converted = fraction of height fallen $=\frac{1}{2}$.

Answer: (A) $\frac{1}{2}$

Concept: Power is the rate at which energy is transferred or work is done.

1. $P=\frac{E}{t}$; SI unit watt $=\text{J/s}$.
2. $E\times t$, $E+t$ or $\frac{E}{t^2}$ do not have the unit of watt, so they are wrong.

Yaad rakhein: Watt = joule per second → $P=\frac{E}{t}$.

Answer: (A) $P=\frac{E}{t}$

Concept: In series the same current $I$ flows through both resistors, so $P=I^{2}R$ gives $P\propto R$.

1. $\frac{P_1}{P_2}=\frac{I^2{R}_1}{I^2{R}_2}=\frac{R_1}{R_2}$.
2. $P_1=4P_2\Rightarrow R_1:R_2=4:1$.

Trick: Series → $P\propto R$; parallel → $P\propto \frac{1}{R}$ (then the answer would be $1:4$).

Answer: (D) 4 : 1