Bihar Board - Class 12 Physics - Chapter 3: Current Electricity Short Answer Question
Short Answer Type Questions
1. Using the mathematical expression for the conductivity of a material, explain how it varies with temperature for
(i) semiconductors, (ii) good conductors.
Answer:
Conductivity σ = ne2m
(i) Semiconductors: With increase in temperature, conductivity of semiconductor increases. It is due to increase in V. It dominates the effect caused by decrease in ‘x’.
(ii) Good conductors : With increase in temperature, conductivity of good conductors decreases. It is due to a decrease in the value of relaxation time. The effect of increased value of V is negligible.
2. A cell of emf ‘E’ and internal resistance V is connected across a variable resistor ‘R’. Plot a graph showing the variation of terminal potential ‘V’ with resistance R.
Predict from the graph the condition under which ‘V’ becomes equal to ‘E’.
Answer:
(i) V = ε – Ir gives the terminal voltage and can be plotted as shown in Figure 1.
(ii) The graph between V and R, is shown in Figure 2.
V becomes E when no current is down.
3. Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.
Answer:
In the absence of an electric field the electrons motion is random and the net velocity is zero. In the presence of electric fields, they tend to flow opposite to that of the electric field in the conduction. If an electric field ‘E’ is applied across a length l of the conductor, the electrons will experience an acceleration, a = eEm
If the average time for the acceleration is x, the velocity required is
Vd = u +a = a
Vd = - eEm
Vd = eEm
4. A wire of 20 Ω resistance is gradually stretched to double its original length. It is then cut into two equal parts. These parts are then connected in parallel across a 4.0 volt battery. Find the current drawn from the battery.
Answer: On stretching, the resistance of the wire will get to four times, i.e., 80 Ω as volume is constant and
R∝ l2
So the two equal parts will have a resistance of 40 Ω each.
When connected in parallel, the equivalent resistance will be 20 Ω
∴ Current drawn = VReq = 420 = 15 = 0.2 A
5.In the given circuit, assuming point A to be at zero potential, use Kirchhoff’s rules to determine the potential A at point B.
Answer: Applying Kirchhoff’s law by moving along ACDE,
we get,
6. Define mobility of a charge carrier. Write the relation expressing mobility in terms of relaxation time. Give its SI unit.
Answer: Mobility:- Mobility of electron p is defined as the magnitude of the drift velocity per unit electric field E
∴ = VdE = em
and S.I. unit : m2V-1S-1
7. State Kirchhoff’s rules. Explain briefly how these rules are justified.
Answer:
Kirchhoff’s rules.
1. Kirchhoff’s junction rule : At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving the junction.
2. Kirchhoff’s loop rule : The algebraic sum of changes in potential in any closed loop involving resistors and cells is zero.
These two laws are justified on the basis of law of conservation of charge and the law of conservation of energy respectively.
8. Distinguish between emf (ε) and terminal voltage (V) of a cell having internal resistance r. Draw a plot showing the variation of terminal voltage (V) vs the current (I) drawn from the cell. Using this plot, how does one determine the internal resistance of the cell?
Answer: emf is the potential difference between two terminals of the cell, when no current is drawn from the cell I while
• Terminal voltage is the potential difference between two terminals when current passes through it.
• The negative slope of the graph gives internal resistance.
9. Use Kirchhoff’s rules to determine the potential difference between the points A and D when no current flows in the arm BE of the electric network shown in the figure.
Answer:
Let us consider the loop ABED.
Using Kirchhoff’s second law, we have
VAD =(6V+3V)+IR1
= 9V + 0 =9V ………………………..(I is zero in BE arm)
10. Bends in a pipe slow down the flow of a liquid through that pipe. Do bends in a conductor increase its electrical resistance? Give a reason.
Answer:
No, the bends in a conductor do not increase its electrical resistance because free electrons are of extremely small dimensions as compared to bends and hence, they can easily adjust their flow direction.
11.In what respect, does a nearby discharged electrochemical cell differ mainly from a freshly prepared cell in its emf or in its internal resistance?
Answer: The cell mainly differs in its internal resistance. A freshly prepared cell has an extremely low internal resistance of the order of a fraction of one ohm. However, a nearly discharged cell has a high internal resistance of a few hundred ohms.
12. What are the advantages of the null-point method in a Wheatstone bridge? What additional measurements would be required to calculate Runknown by any other method?
Answer: In the case of a Wheatstone bridge, the technique of null point uses balanced Wheatstone bridges, in which the galvanometer’s resistance does not influence the balance point. There is no requirement to find the currents in the galvanometer and resistances. The unbalanced Wheatstone bridge can also be utilized to determine the unknown resistance. However, in this technique, we need the additional accurate measurement of every current in the galvanometer and resistors as well as the galvanometer’s internal resistance.
13. What is the advantage of using thick metallic strips to join wires in a potentiometer?
Answer: Resistance is given by the relation
R = lA
So, as the cross-sectional area of the wire increases, the resistance of the wire reduces. Therefore, the metal strips possess very low resistance and can be easily neglected while determining the wire’s length used to find the null point.
14. For wiring in the home, one uses Cu wires or Al wires. What considerations are involved in this?
Answer: In the case of electrical wiring in houses, two factors are involved while choosing the wiring materials, the cost of the conducting material (in most cases metal) and the conductivity of the wire. Silver has the greatest conductivity, but it is generally ignored due to its high cost. Just after silver, aluminum and copper are the next ideal conductors. Their production cost is also lower than silver. Thus, aluminum and copper are used for electrical wiring in houses.
15. Why are alloys used for making standard resistance coils?
Answer: Alloys are employed for constructing conventional resistance coils as they possess high resistivity and a small resistivity temperature coefficient.
16. It is easier to start a car engine on a warm day than on a chilly day. Why?
Answer: On a warm day, room temperature is higher and with rise in temperature, the internal resistance of the car battery decreases. As a result, the car battery can provide a greater current and the car engine will start easily.
17. Is the motion of a charge across junction momentum conserving? Why or why not?
Answer: If the motion of a charge is occurring across a junction, the momentum of the charge is not at all conserved. This is because when the charge (electron) approaches the junction, apart from the uniform electric field that it typically encounters (which maintains the drift velocity fixed), there will be an accumulation of charges on the wires’ at the junction. This also generates an electric field, enabling the change in the direction of the charge’s momentum.
18. Light from a bathroom bulb gets dimmer for a moment when the geyser is switched on. Explain why?
Answer: When the geyser is switched on, it draws a large current. Although the light bulb and geyser are in parallel, for a moment, the voltage of the circuit is lowered on account of the large current drawn by the geyser. Consequently, the bathroom bulb gets dimmer. However, within a short time, the voltage is stabilized by the transmission grid and so, the bulb starts glowing fully at its normal rate.
19. In a meter bridge experiment, why is it considered important to obtain the balance point near the midpoint of bridge wire?
Answer: The sensitivity of a Wheatstone bridge is maximum when all the four resistance P, Q, R and S are equal or nearly equal. For this purpose, we consider it important that the null point is obtained near the mid-point of bridge wire so that lengths l and (100-l) and consequently, their resistance P and Q are almost equal.
20. Is a current carrying conductor charged? Give a reason.
Answer: In a current carrying conductor, charge carries flow such that net inflow rate is exactly equal to net outflow rate at any cross-section. Consequently as a whole, there is no net charge on the conductor.
21.Does electric current change with change in its cross-section for a conductor of variable cross-section?
Answer: No, for a given conductor, current does not change with change in cross-section. It is because electric charge is conserved and electric current is the rate of flow of charge. The charge entering per unit time at one end of the conductor is exactly equal to the charge leaving per unit time at the other end.
22. The electron drift speed is estimated to be only a few mm/s for currents in the range of a few amperes. How is current established almost the instant a circuit is closed?
Answer: As soon as a circuit is closed, an electric field is established throughout the circuit almost instantly causing at every point a local electron drift. Establishment of a current does not have to wait for electrons from one end of the conductor to travel up the other end.
23. Two heating coils, one of fine wire and other of thick wire, made of the same material and the same length are connected one by one to a source of electricity. Which one of the two coils will dissipate electric power at a greater rate?
Answer: When a heating coil of residence R is connected to a source of electricity of voltage V, the power dissipated,
P = V2R
As thicker wire has less resistance than a thin wire, power dissipated in thicker wire will be more than in a fine wire.
24. A metallic conductor is initially at a temperature T1. Then, its temperature is increased to T2. Will the product of its resistivity and conductivity change?
Answer: The product of resistivity (ρ) and conductivity (σ) of a metallic conductor remains constant at all temperatures having a value ρ.σ = 1. As the temperature of a metallic conductor is raised, its resistivity rises and in turn, conductivity falls but their product remains unchanged at 1.
25. Does the value of resistance of a conductor depend upon the potential difference applied across it or the current passed through it?
Answer: No, the resistance of a conductor does not depend upon either the potential difference applied across it or the current being passed through it. If the potential difference applied across a conductor is also proportionally increased such that their ratio V/I, i.e. the resistance R of the conductor remains constant.
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