# CBSE Class 12 Physics HOTs Current Electricity

## Chapter 3 Current Electricity Class 12 Physics HOTS

Class 12 Physics students should refer to the following high order thinking skills questions with answers for Chapter 3 Current Electricity in Class 12. These HOTS questions with answers for Class 12 Physics will come in exams and help you to score good marks

### HOTS Questions Chapter 3 Current Electricity Class 12 Physics with Answers

UNIT 02

CURRENT ELECTRICITY

ONE MARK QUESTIONS

Question. Define the terms conductivity of a conductor?On what factors do it depend?
Answer : Conductivity is the reciprocal of resistivity,It depends upon no density of electrons and Average relaxation time.

Question. V – I graph for a metallic wire at two different temperatures T1 and T2 is as shown in the figure. Which of the two temperatures is higher and why?

Answer : For metallic wire R=V/I increases with temperature, hence T1 will be higher.

Question. A 10 V battery of negligible internal resistance is connected across a 200 V battery and a resistance as shown in the figure find the value of current in the circuit.

Question. When electrons drift in a metal from lower to higher potential, does it mean that all the free electrons of the metal are moving in the same direction?
Answer : No, Maximum no of electrons will drift opposite to the direction of higher potential

Question. Show on a graph the variation of resistivity with temperature for a typical semiconductor?

Question. Two metallic resistors are connected first in series and then in parallel across a d.c. supply. Plot of I – V graph is shown for the two cases. Which one represents a parallel combination of the resistors and why?

Answer : In parallel combination less resistance will be the equivalent resistance, therefore A will represent parallel combination.

TWO MARKS QUESTIONS

Question. Calculate the current drawn from the battery by the network of resistors shown in figure

Answer : As the circuit is similar to a whaetstone bridge 5 Ω resistor can be removed ,then R=2Ω
Hence i=2 amp.

Question. Using the concept of drift velocity of charge carriers in a conductor, deduce the relationship between current density and resistivity of the conductor.
Answer :  j= I/A = n e V d j =σ E =1/ρE

Question. A variable resistor R is connected across a cell of emf E and internal resistance r as shown in the figure. Draw a plot showing the variation of (i) terminal voltage V and (ii) the current I, as a function of R. (Image 4)

Question. Two electric bulbs P and Q have their resistances in the ratio of 1: 2. They are connected in series across a battery. Find the ratio of the power dissipation in these bulbs.
Answer : P = V2/R hence the ratio will be 2:1

THREE MARKS QUESTIONS

Question. A 16 Ω resistance wire is bent to form a square. A source of emf 9 V is connected across one of its sides as shown. Calculate the current drawn from the source. Find the potential difference between the ends C and D.
If now the wire is stretched uniformly to double the length and once again the same cell is connected in the same way, across one side of the square formed, what will now be the potential difference across one of its diagonals?

Question. A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current I.
It is found that when R = 4 , the current is 1 A and when R is increased to 9 , the current reduces to 0.5 A. Find the values of the emf E and internal resistance r.

Question. A potential difference V is applied across a conductor of length L and diameter D. How is the drift velocity, Vd, of charge carriers in the conductor affected when (i) V is halved, (ii) L is doubled and (iii) D is halved? Justify your answer in each case.
Drift velocity halved
Drift velocity halved

Question. A resistance R draws current from a potentiometer, the potentiometer AB, has a total resistance R, a voltage V is applied to the potentiometer.
Derive an expression for the voltage across R when the sliding contact is in the middle of potentiometer wire.

FIVE MARKS QUESTIONS

Question. Use Kirchhoff’s rules , calculate the current in the arm AC of the given circuit
On what principle does the meter bridge work? Why are the metal strips used in the bridge?
Answer : I1 = -12/13 A
I2 = -8/13 A
I1+ I2 = -8/13 + -12/13=-20/13A

Question. In the figure a long uniform potentiometer wire AB is having a constant potential gradient along its length. The null points for the two primary cells of emfs E1and E2 connected in the manner shown are obtained at a distance of 120 cm and 300 cm from the end A.
Find E1 / E2 and position ofnull point for the cell E1.
How is the sensitivity of a potentiometer increased?
210cm

Question. Draw a circuit diagram of a potentiometer .State its working principle. Derive the necessary formula to describe how it is used to compare the emfs of the two cells.
Write two possible causes for one sided deflection in a potentiometer experiment.
Answer : E1/E2 = l1/l2 (derive it)
The emf of the driver cell may be less than the secondary cell
Very high resistance connected in series with the drver cell circuit

One mark questions

Q1.Under what conditions will Terminal potential difference of a cell be greater than its EMF?

Q2.A wire of resistivity p is stretched to twice its length. What will be its new resistivity?

Q3.Give the colour coding for a carbon resistor of 1 ohm having 5% tolerance?

Q4.If the temperature of a metallic conductor increases how does the relaxation time of electrons in conductor change?

Q5. Write the dimensional formula of mobility of electrons.

Q6.Manganin is used in making standard resistance .give two reasons.

Q7.How does the drift velocity of electrons in a metallic conductor change, if the length of the conductor is doubled by stretching it, keeping the applied potential difference constant?

Q8.The variation of potential difference V with length l in case of two potentiometers ‘a’ and ‘b’ is shown in the graph given below.
Which one of these two will you prefer for comparing EMF of two cells? Give reason.

Q9. Why the terminal Potential is always less than EMF of a cell, while in use?

Q10. The conductivity of a semi conductor increases with the rise of temperature. Give reason. Two Marks Questions

Q11.N number of identical resistors each of resistance R is combined to get the maximum and minimum resistances, what is the ratio of the maximum to minimum resistance.

Q12.Two wires of equal length one of copper and other of manganin have same resistance. Which of the two wires will be thicker? Justify your answer with the help of suitable formula.

Q13.A resistor of 24 ohm resistance is bent in the form of a loop as shown in the figure. Calculate effective resistance between points A and B?

Q14.V-I graph for metallic wire at two different temperature ‘a’ and ‘b’ is shown in fig. Which of the two temperatures is higher and why?

Q15. Explain why the I-V characteristics of a resistor are obtained to deviate from a straight line from higher values of current as shown below:

Three Marks Question-
Q16.Two resistances are in the ratio 1:4 if these are connected in parallel their total resistance becomes 20 ohm. Find the value of each resistance.

Q17.A household circuit has a fuse of 5A rating. Calculate the maximum number of bulbs of rating 60W-220V each which can be connected in the household circuit.

Q18. Calculate current in each branch.

Q19.Two identical cells of EMF E and internal resistance r whether joined in series or in parallel give the same current, when connected to external resistance of 1 ohm. Find internal resistance of each cell.

Q20. 4 cells of identical EMF E, internal resistance r are connected in series to a variable resistor. The following graph shows the variation of terminal voltage of the combination with the current output:
1.What is the EMF of each cell?
2.calculate the internal resistance of each cell.

1. during charging
2. uncharged
3. black, brown, black (gold)
4. decreases
5. ML3T-4A-1
6. Low temp. Coefficient of resistance high Resistivity.
7. drift velocity halved
8. kb<ka (k is the potential gradient)
9. T.P. =EMF - Ir
10. Due to increase in carrier density

Two Marks-
11. N2:1
12. MANGANIN
13. 10/3 OHM
14. a>b
15. temp. increases
slope decreases
ohm law is disobeyed

Three Marks-
16. R1=25 ohm
R2=100 ohm
17. no. of bulb=18
18 .I1=5/2A
I2=5/8A
I3=7/8A
19 r=1 ohm
20. (1)E=1.4 V
(2)r=0.7 ohm.
Current Electricity
1. In a hydrogen atom, an electron moves in an orbit of radius 4.8 x 10-11m with a speed of 2.5 x 106 m/s. Find the equivalent current.

2. Plot of current I versus time interval is given below. Find the charge that flows through the wire during this time period.
3. Amount of charge passing through the cross section of a wire is q(t)=at2+bt+c.Write the dimensional formula for a, b and c. If the values of a, b and c in SI unit are 6, 4, 2 respectively. Find the value of current at t=6 seconds.

4. Current through a wire depends on time as I=I0+αt where I0 =15A and α=6 A/s.Find the charge that flows across a section of wire in 12 seconds.

5. One metre long metallic wire is broken into two equal parts P and Q. The part ‘P’ is uniformly extended into another wire R. Length of R is twice the length of P and the resistance of R is equal to that of Q. Find the ratio of the resistances of P and R and also the ratio of lengths of P and Q.

6. The area of cross section , length and density of a piece of a metal of  atomic weight 60 are 10-6 m2, 1.0 m and 5 x 103 kg/m3 respectively . Find the number of free electrons per unit volume of every atom that contributes one free electron. Also find the drift velocity of electron in the metal when a current of 16A passes through it. Avogadro no.=6x1023 per gram per mole.
7. An n-type Silicon sample of width 4x 10-3 m thickness 25x10-4m and length 6 X 10-2 m carries a current of 4.8mA.When the voltage is applied across the length of the sample what is the current density? If the free electron density is 1022 /m3 then find how much time does it take for the electrons to travel the full length of the sample?

8. The temperature coefficient of a resistance wire is 0.00125 C-1. At 300K its resistance is 1Ω. At what temperature the resistance of the wire will be 2Ω.?

9. The length and radii of 3 wires of same metal are in the ratios 2:3:4 and 3:4:5 respectively. They are joined in parallel and included in a circuit having 5A current. Find the current in each case.

10. In the circuit diagram the voltmeter reads 30V when connected across 400Ω resistance. Calculate  reading in the same voltmeter when it is connected across 300Ω resistance?
11. A galvanometer together with an unknown resistance in series is connected across 2 identical cells each of emf 1.5V. When the cells are connected in series the galvanometer records a current of 1A and when the cells are connected in parallel the current is 0.6 A .What is the internal resistance of each cell?

12. An electric bulb rated for 500 Watt at 100 V is used in circuit having a 200 V supply. Calculate the resistance R that must be put in series with the bulb s that the bulb delivers 500 watt.

13. A heater is designed to operate with a power of 1000 watt in a 100 V line. It is connected in combination with a resistance of 10 and a resistance R, to a 100 V mains in series. What should be the value of ‘R’ so that the heater operates with a power of 62.5 watt

14. An electric kettle has 2 heating coils. When one of the coils is switched on , the kettle begins to boil in’6’ min and when the other coil is switched on , the boiling begins in 8 min. In what time will the boiling begin if both the coils are switched on simultaneously : a)in series b)in parallel.

15. One kilowatt electric heater is to be used with 220 V d.c supply. a)What is the current in the heater? b) What is its resistance? c) What is the power dissipated in the heater d) how much heat in calories is produced per second? e) How many grams of water at 1000C will be converted per minute into steam at 1000C with the heater? Radiation losses are negligible. Latent heat of steam = 540 cal /g.

16. The walls of a closed cubical box of edge 50 cm are made of a material of thickness 1mm and thermal conductivity 4x10-4 cal per sec per cm. per oC. The interior of the box maintained at 1000C above the outside temperature by a heater placed inside the box and connected across a 40V d.c source .Calculate the resistance of the heater.

17. A part of the circuit in a steady state along with the currents following in the branches, the values of the resistance etc is shown in the fig. Calculate the energy stored in the capacitor.
19.A potentiometer wire of length 100 cm has a resistance of 100Ω ,it is connected in series with a resistance and a battery of emf 2V and of negligible internal resistance. A source of emf 10mV is balanced against a length of 40cm of the potentiometer. What is the value of the external resistance?

20.A battery of internal resistance r=4Ω is connected to the network  of resistence as shown in figure. What must be the value of R , so that maximum power is delivered to the network? What is the maximum power?
21. A battery of emf 2V and internal resistance 0.1 Ω is being charged by a current of 5A. What will be the direction of current inside the battery? What is the potential difference between the terminals of the battery?

22. Two wires A and B of the same material and having same length have their cross sectional area in the ratio1:4. What would be the ratio of heat produced in these wires when same voltage is applied across each?

23. Two wires of the same material having lengths in the ratio 1:2 and diameters in the ratio 2:3 are connected in series with an accumulator. Compute the ratio of p.d across the two wires.

24. If the current supplied to a variable resistor is constant, draw a graph between voltage and resistance.

25. Observations on a given device yielded the following current – voltage data.
Current (A)                               Voltage
1                                              19.7
2                                              39.4
3                                              59.1
4                                              78.8
5                                              98.5
Draw V-I graph using this data. What conclusion can you draw from the graph with regard to ohmic or non-ohmic nature of device?

26. Current voltage graphs for a given metallic wire at different temperatures T1 and T2 are shown in figure. Which of the temperatures T1 and T2 is greater?
27. V-I graphs for two resistors and their series combination are as shown in figure. Which one of these graphs represents the series combination of the other two? Give reasons for your answer.

28. Two metallic wires of the same material and same length but of different cross sectional areas are joined together.
1) in series
2) in parallel to a source of emf.
In which of the two wires will the drift velocity of electron be more in each of the two cases and why?

29. The resistivity of a material of a conductor of uniform cross section varies along its length as e=ε (1+αx). deduce the expression for the resistance of the conductor, if its length is “L” and area of cross section is “A”.

30. A uniform wire of resistance “R” is shaped into a regular “n” sided polygon, where “n” is even. Find the equivalent resistance between
1) opposite corners of the polygon
2) adjacent corners of the polygon.

31. Under what condition is the heat produced in an electric circuit
1) directly proportional
2) inversely proportional to the resistance of the circuit?

32. A 4Ω non insulated wire bent 1800 in the middle and the two halves are twisted together. What will be its new resistance?

33. What is the safest voltage you can safely put across a 98Ω, 0.5 watt resistor?

34. A student has two wires of iron and copper of equal length and diameter. He first joins the two wires in series and passes electric current through the combination which increases gradually. After that he joins the two wires in parallel and repeats the process of passing current. Which wire will glow first in each case and why?

35. A series combination of a 2KΩ  resistor and 1KΩ resistor is connected across a battery of emf 6V and negligible internal resistance. The potential drop across the 2Ω resistor is measured by
1. a 30KΩ voltmeter
2. a 1KΩ voltmeter
3. both these voltmeters connected across it.

If the voltmeter readings in the three cases are V1, V2 and V3 respectively,arrange these readings in descending order.
How will the three readings be compared with one another if the potential drop were measured across the series combination of the 2 K Ω and 1 K Ω resistor?i.e. across A and B?

CURRENT ELECTRICITY

1. Magnesium is used for making standard resistors, why?

2. The sequence of bands marked on a carbon resistor are: Red, Red, Red, Silver. Write the value of resistance with tolerance.

3. A wire of resistively ρ is stretched to three its initial length, what will be its new resistively.

4. If p.d.v applied across a conductor is increased to 2v, how will the draft velocity of the electrons change?

5. A 10Ω thick wire is stretched so that its length becomes three times. Assuming thatthere is no change in its density on stretching. Calculate the resistance of new wire.

6. You are given 8 Ω resistor. What length of wire of resistance 120 Ωm-1 should be joined in parallel with it to get a value of 6 Ω ?

7. Three resistance 3Ω,6Ω and 9Ω are connected to a battery. In which of them will the powerdissipation be maximum if

a) They are all connected in parallel

b) They are all connected in series Give reason.

8. A silver wire has a resistance of 2.1Ω at 27.5˚c and a resistance of 2.7Ω at 100˚c. determine the temperature coeff. of resistivity of silver.

9. Give any two applications super conductors.

10. Two wire of equal length one copper and manganin have same resistance , which wire is thicker?.

11. Why manganin is used for making standard resistor?

12. A copper wire of resistivity r is stretched to reduce its diameter to half of its previous value .What  will be the new resistances?

13. The variation of potential difference with length incase of two potentiometres A and B is given below.Which of the two is more sensitive.

14. If the length of the wire conductor is doubled by stretching it , keeping potential difference constant by what factor the drift speed of the electron changed.

15. If the temperature of the conductor increases, how does the relaxation time of electron changes.

16. A heater joined in series with the 60W bulb .With change of bulb with 100 W in the circuit, the rate heat produce by the heater will more or less or remain same.

17. What will be the change in the resistance of the circular wire , when its radius is halved and length is reduced by ¼ th of original length.

18. Two 120V light bulbs , one of 25W and another of 200W are connected in series . One bulb burnt out almost instantaneously ?.Which one was burnt and why?.

19. A given copper wire is stretched to reduce its diameter is half of its original value.What will the new resistance?.

20. A student has two wire of iron and copper of equal length and diameter.He first joins two wires in series and pass electric current through the combination which increases gradually.After that he joins two wires in parallel and repeats the process of passing current.Which wire will glow first in each case?

21. A cylindrical metallic wire is stretched to increase its length by 5% . Calculate the percentage change in resistances.

22. A wire of resistance 4R is bend in the form of circle .What is the effective resistance between the ends of diameter?.

23. Two wires A and B have same lengths and material , have their cross sectional areas 1:4 , what would be the ratio of heat produced in these wires when the voltage across each is constant.

24. Two bulbs whose resistance are in the ratio of 1:2 are connected in parallel to a source of constant voltage. What will be the ratio of power dissipation in these?

25. Total resistance of the circuit is R/3 in which three identical resistors are connected in parallel. Find the value of each resistance?
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