CUET UG Physics Booster Test – 2 Material Properties and Power

Ohm's law states that the potential difference across a conductor is directly proportional to the current flowing through it, provided physical conditions remain constant. Under these conditions, the ratio V/I remains constant and is called resistance. In a non-linear device, the V-I graph is not a straight line. Therefore, the ratio V/I changes with voltage or current. This means the resistance is not constant and varies depending on the operating point of the device. Semiconductor devices such as diodes commonly exhibit such behavior. Since the resistance changes with the applied voltage or current, the device does not obey Ohm's law over its entire operating range. Hence, the correct answer is B.

Certain electrical devices, especially semiconductor diodes, behave differently when the direction of the applied voltage is reversed. In forward bias, a large current may flow, while in reverse bias only a very small current exists. Thus, reversing the voltage does not simply reverse the current with the same magnitude. This sign-dependent behavior is one of the important limitations of Ohm's law because Ohm's law assumes a linear and symmetric relationship between voltage and current. Ordinary metallic conductors such as copper exhibit nearly identical resistance for both directions of current and therefore do not display this sign-dependent behavior. Hence, statements 1 and 2 are correct, while statement 3 is incorrect.

A diode is a non-Ohmic device whose current-voltage characteristic is strongly dependent on the direction of the applied voltage. When forward biased, the diode allows significant current to flow after a threshold voltage is reached. When reverse biased, only a very small leakage current flows. Therefore, the current obtained for positive voltage is drastically different from the current obtained for negative voltage. This asymmetrical and non-linear behavior demonstrates that the diode does not obey Ohm's law. Hence, observation B directly confirms the non-Ohmic nature of the diode.

Gallium Arsenide (GaAs) is a semiconductor material that can exhibit non-linear and non-unique current-voltage characteristics. In certain operating regions, the V-I curve bends in such a way that the same current value corresponds to more than one voltage value. This behavior is impossible for a simple Ohmic conductor, where every current value corresponds to exactly one voltage value according to V=IR. Therefore, non-uniqueness means that a single current can be associated with multiple voltage values.

Metals are characterized by very low resistivity values, typically ranging from about 10^(-8)to 10^(-6) Ω m. This low resistivity arises because metals possess an enormous number of free electrons available for conduction. The number density of free electrons in metals is typically of the order of 10^(28)to 10^(29) m^(-3), which allows large currents to flow even when the drift velocity is very small. Since metals conduct electricity efficiently, they are classified as conductors rather than insulators. Therefore, statement 2 and statement 3 are correct, while statement 1 is incorrect.

High resistivity materials, commonly called insulators, strongly oppose the flow of electric current. Examples include ceramic, rubber, plastics, glass, and mica. Their resistivities are enormously larger than those of metals, often by factors of 10^(18)or more. The fundamental reason for this behavior is that electrons in insulators are tightly bound to their parent atoms and cannot move freely under ordinary electric fields. Consequently, the number of mobile charge carriers available for conduction is extremely small. Statement C is incorrect because metals actually possess a much larger density of free charge carriers than insulators. The scarcity of mobile carriers is precisely why insulators exhibit such high resistivity.

The temperature coefficient of resistivity αmeasures the fractional change in resistivity per unit change in temperature. It appears in the relation ρ_T=ρ_0[1+α(T-T_0)] For most metallic conductors, αis positive. Therefore, an increase in temperature leads to an increase in resistivity because lattice vibrations become stronger and hinder electron motion. Since αrepresents change per unit temperature, its unit is the reciprocal of temperature, namely K^(-1)or ^∘C^(-1). It is not measured in Ω/K. Thus, statements 1 and 2 are correct while statement 3 is incorrect.

Using R=R_0[1+α(T-T_0)] Given: R_0=100ΩR=102Ωα=2×10^(-4) ^∘C^(-1) Substituting: 102=100[1+2×10^(-4)(T-27)]1.02=1+2×10^(-4)(T-27)0.02=2×10^(-4)(T-27)T-27=100T=127^∘C Hence the correct answer is 127^∘C.

Metals possess a positive temperature coefficient of resistivity. Therefore, when the temperature of a metallic conductor rises, its resistivity increases due to enhanced lattice vibrations that obstruct electron motion. Since R=ρl/A an increase in resistivity causes resistance to increase. For a fixed applied voltage, I=V/R Thus, as resistance increases, the current decreases. This effect is commonly observed in filament lamps and heating elements during operation. Hence, the correct answer is that resistance increases while current decreases.

The expression ρ_T=ρ_0[1+α(T-T_0)] is an approximate linear relation valid only over a moderate temperature range. For metals such as copper, experimental observations show that resistivity does not continue to vary linearly at very low temperatures. As the temperature approaches low values, the resistivity-temperature curve deviates significantly from a straight line. In this region, a single constant value of αcannot accurately describe the variation of resistivity. Therefore, the low-temperature behavior is non-linear and requires more detailed physical models than the simple linear approximation.

Nichrome is an alloy of nickel, chromium, and iron that exhibits only a weak dependence of resistivity on temperature. As the heating element becomes hot during operation, its resistance changes only slightly compared to ordinary metallic conductors. This property is highly desirable because it allows the heating element to operate predictably over a wide temperature range. A large change in resistance would lead to significant fluctuations in current and power consumption. Therefore, nichrome is widely used in toasters, electric irons, and heating coils because its resistance remains relatively stable even at high temperatures.

Wire-bound standard resistors are designed to provide highly stable and accurate resistance values. For this reason, materials such as manganin and constantan are used because they possess very small temperature coefficients of resistivity. A small temperature coefficient ensures that minor changes in environmental temperature produce negligible changes in resistance. This stability is essential in precision electrical measurements and calibration instruments. Statement 1 is therefore correct. Statement 3 is also correct because maintaining a constant resistance value is the primary objective of standard resistors. Statement 2 is incorrect because materials with large resistance variations would make accurate measurements impossible.

In semiconductors, increasing temperature excites more electrons from the valence band into the conduction band. This creates a much larger number of free charge carriers. As a result, the carrier density n increases dramatically with temperature. Although the relaxation time τmay decrease because collisions become more frequent, the increase in carrier density is much greater. Consequently, conductivity increases and resistivity decreases. Therefore, statement D is incorrect because intrinsic carrier density is strongly temperature dependent and certainly does not remain constant.

The conductivity of a semiconductor is given by σ=ne^2τ/m As temperature increases, lattice vibrations become stronger, causing more collisions and reducing the relaxation time τ. However, temperature also generates a very large number of additional charge carriers. The increase in carrier density n is far greater than the decrease in τ. Consequently, the overall conductivity increases and the resistivity decreases. Thus, the dominant factor responsible for the reduction in resistivity is the dramatic rise in carrier density.

The potential gradient is defined as the rate at which potential decreases along the length of a conductor. Mathematically, Potential Gradient=V/l For a resistor obeying Ohm's law, V=IR Substituting into the expression for potential gradient, V/l=IR/l This quantity represents the potential drop per unit length of the conductor and is directly related to the electric field inside the conductor.

When charge moves through a conductor, electrical potential energy decreases. The energy lost during time Δt is ΔU_(pot)=-IVΔt Therefore, 1 → d. In an ideal energy accounting process, total energy remains conserved, so the total internal electrical energy change is unchanged, giving 2 → c. If charges could move without collisions, the electric field would continuously accelerate them and their kinetic energy would increase by +IVΔt Thus, 3 → b. In a real conductor, electrons undergo frequent collisions with lattice ions. As a result, the average drift velocity remains constant and there is no net increase in kinetic energy. Therefore, 4 → a. Hence the correct matching is: 1-d, 2-c, 3-b, 4-a

In a conductor carrying current, free electrons are accelerated by the electric field between successive collisions. During collisions with lattice ions, a portion of the gained kinetic energy is transferred to the lattice. This transfer increases the vibrational energy of the ions. As lattice vibrations become more intense, the temperature of the conductor rises. This phenomenon is observed as Joule heating. Therefore, electrons continuously gain energy from the electric field and transfer it to the lattice through collisions. The net result is the conversion of electrical energy into thermal energy. Hence statements 1, 2, and 3 are all correct.

Electrical energy dissipated as heat is given by W=VIΔt Given: V=220VI=5AΔt=10s Substituting, W=220×5×10W=11000J Thus the heating element converts 11,000 joules of electrical energy into thermal energy during the 10-second interval.

Electrical power is defined as the rate at which electrical energy is supplied or dissipated. Mathematically, P=VI Therefore, power depends directly on both voltage and current. The energy required to maintain current flow is supplied by an external source such as a battery, generator, or power supply. Statement 3 is incorrect because power represents the rate of energy transfer per unit time, not the total energy transferred during the entire operation of a circuit. Hence statements 1 and 2 are correct.

The power transmitted is P=VI Therefore, I=P/V The power dissipated in the transmission cable is P_c=I^2R_c Substituting the value of current, P_c=(P/V)^2R_cP_c=P^2R_c/V^2 This equation explains why electrical power is transmitted at very high voltages. Increasing V reduces current and therefore greatly reduces transmission losses.