This question tests the fundamental characteristics of an ideal operational amplifier (op-amp). An ideal op-amp is a theoretical model used to simplify analysis and understand the basic behavior of op-amp circuits. One of its key characteristics relates to its input impedance.
Correct Option: B) infinity
The efficiency of a rectifier is defined as the ratio of the DC output power to the AC input power. For a bridge rectifier, we need to derive the expressions for both output DC power and input AC power, and then calculate their ratio. The maximum theoretical efficiency is achieved under ideal conditions.
Define Efficiency: The efficiency \(\eta\) of a rectifier is given by:
\[ \eta = \frac{P_{dc}}{P_{ac}} \]where \(P_{dc}\) is the DC output power and \(P_{ac}\) is the AC input power.
Calculate DC Output Power (\(P_{dc}\)): For a full-wave rectifier (which includes the bridge rectifier), the average (DC) output voltage \(V_{dc}\) and current \(I_{dc}\) are:
\[ V_{dc} = \frac{2V_m}{\pi} \]\[ I_{dc} = \frac{2I_m}{\pi} \]where \(V_m\) and \(I_m\) are the peak values of the AC voltage and current, respectively. The DC output power is:
\[ P_{dc} = V_{dc} I_{dc} = \left(\frac{2V_m}{\pi}\right) \left(\frac{2I_m}{\pi}\right) = \frac{4V_m I_m}{\pi^2} \]Calculate AC Input Power (\(P_{ac}\)): The AC input power is the RMS voltage multiplied by the RMS current. For a sinusoidal input, the RMS values are:
\[ V_{rms} = \frac{V_m}{\sqrt{2}} \]\[ I_{rms} = \frac{I_m}{\sqrt{2}} \]The AC input power is:
\[ P_{ac} = V_{rms} I_{rms} = \left(\frac{V_m}{\sqrt{2}}\right) \left(\frac{I_m}{\sqrt{2}}\right) = \frac{V_m I_m}{2} \]Calculate Efficiency (\(\eta\)): Now, substitute \(P_{dc}\) and \(P_{ac}\) into the efficiency formula:
\[ \eta = \frac{P_{dc}}{P_{ac}} = \frac{\frac{4V_m I_m}{\pi^2}}{\frac{V_m I_m}{2}} = \frac{4V_m I_m}{\pi^2} \times \frac{2}{V_m I_m} = \frac{8}{\pi^2} \]Convert to Percentage: To express the efficiency as a percentage, multiply by 100:
\[ \eta_{\%} = \frac{8}{\pi^2} \times 100 \]Using the value of \(\pi \approx 3.14159\):
\[ \pi^2 \approx (3.14159)^2 \approx 9.8696 \]\[ \eta_{\%} = \frac{8}{9.8696} \times 100 \approx 0.81056 \times 100 \approx 81.056\% \]Rounding to one decimal place, the maximum theoretical efficiency is approximately 81.1% or 81.2%.
D) 81.2% is the closest and most commonly accepted theoretical maximum efficiency for a full-wave (including bridge) rectifier.
Avalanche breakdown is a phenomenon observed in semiconductor devices, particularly in reverse-biased p-n junctions. It is characterized by a rapid increase in current due to carrier multiplication. Understanding the mechanism behind this multiplication is key to identifying the primary dependency.
Correct Option: B) Collision — Avalanche breakdown is primarily dependent on the phenomenon of collision (specifically, impact ionization) where high-energy carriers collide with lattice atoms, generating new electron-hole pairs, leading to a cascading effect and a rapid increase in current.
The question asks about the number of pn junctions in a Unijunction Transistor (UJT). To answer this, we need to recall the basic structure and working principle of a UJT.
Therefore, a UJT contains only one pn junction.
D) 1 pn junction — A UJT is constructed with a single p-type emitter region alloyed into an n-type silicon bar, forming exactly one pn junction.
The question asks to identify the term for a material that exhibits identical properties in all directions. This is a fundamental concept in material science and mechanics of materials, related to the directional dependence of material properties.
The plasticity index (PI) is a measure of the plasticity of a soil, indicating its ability to undergo plastic deformation. It is defined as the difference between the liquid limit (LL) and the plastic limit (PL) of the soil. Understanding the behavior of different soil types with respect to these limits is key to answering this question.
D) Sand — Sand is a coarse-grained soil that does not exhibit plastic properties. Its particles are too large to hold water in a way that allows for plastic deformation. Therefore, its plasticity index is considered to be zero.
The question asks about the effect of increasing the percentage area of tensile steel on the depth of the neutral axis in RCC beams. We need to understand the equilibrium conditions in a reinforced concrete beam and how the forces change with varying steel reinforcement.
Understanding Neutral Axis: The neutral axis (NA) is the axis in a beam where the stress is zero. Above the NA, concrete is in compression, and below it, steel is in tension (assuming concrete takes no tension).
Equilibrium Condition: For a beam to be in equilibrium under bending, the total compressive force must be equal to the total tensile force. That is, \(C = T\).
The compressive force \(C\) is primarily provided by the concrete in the compression zone, and its magnitude depends on the depth of the neutral axis (\(x_u\)) and the properties of concrete.
The tensile force \(T\) is primarily provided by the steel reinforcement, and its magnitude depends on the area of steel (\(A_{st}\)) and its stress (\(f_{st}\)).
\[ C = 0.36 f_{ck} b x_u \] \[ T = 0.87 f_y A_{st} \]Where:
Relating \(A_{st}\) and \(x_u\): From the equilibrium condition \(C = T\):
\[ 0.36 f_{ck} b x_u = 0.87 f_y A_{st} \]Rearranging for \(x_u\):
\[ x_u = \frac{0.87 f_y A_{st}}{0.36 f_{ck} b} \]Effect of increasing \(A_{st}\): From the equation above, it is clear that \(x_u\) is directly proportional to \(A_{st}\). If the percentage area of tensile steel (\(A_{st}\)) increases, then to maintain the equilibrium (\(C=T\)), the compressive force \(C\) must also increase. Since \(C\) is proportional to \(x_u\), an increase in \(C\) means an increase in \(x_u\).
Therefore, as the percentage area of tensile steel increases, the depth of the neutral axis increases.
A) Depth of neutral axis increases. As derived from the equilibrium equation \(C=T\), an increase in the tensile force (due to more steel) must be balanced by an increase in the compressive force, which is achieved by increasing the depth of the neutral axis.
B) Depth of neutral axis decreases. This is incorrect because increasing the tensile steel area increases the total tensile force, which must be balanced by a larger compressive area, thus increasing the neutral axis depth.
C) Depth of neutral axis does not change. This is incorrect. The depth of the neutral axis is directly dependent on the amount of tensile steel, assuming other parameters remain constant.
D) Lever arm increases. The lever arm (\(z\)) is the distance between the resultant compressive force and the resultant tensile force. For a rectangular section, \(z = d - 0.42 x_u\), where \(d\) is the effective depth. Since \(x_u\) increases, \(0.42 x_u\) increases, and thus \(z\) (lever arm) will decrease, not increase.
The question asks for the characteristic property of a fluid regarding its resistance to change. We need to recall the definition of a fluid and its behavior under applied forces, particularly shear stress.
C) Shape — A fluid offers no resistance to a change of shape. When a shear force is applied, it continuously deforms or flows, taking the shape of its container.
The question asks about the composition of an Invar tape. Invar is a specific type of alloy known for its extremely low coefficient of thermal expansion, which makes it suitable for precision measurements like those performed with measuring tapes in surveying.
Correct Option: D) Nickel and steel. Invar is an alloy primarily composed of nickel and iron. Steel is an alloy of iron and carbon, so nickel and steel (iron) accurately describe the main components of Invar.
The question asks about the primary information provided by a Gantt chart. We need to understand the purpose and application of Gantt charts in project management and production planning.
B) Production schedule — A Gantt chart is fundamentally a scheduling tool. It graphically represents the start and end dates of various tasks, their durations, and their interdependencies, making it ideal for managing and visualizing a production schedule. It helps in planning, coordinating, and tracking the progress of production activities over time.