Resistance and resistivity

Resistance: 

The flow of electrons is not so free inside a metallic conductor. Just like  flow of water in a river is opposed by the presence of big rocks in its way, the flow of electrons is similarly opposed by stationary atoms and repulsion by other electrons.

The typical speed of an electron moving inside a metal is of the order of \(10^6\) m/s. It however collides million times in a second and it barely moves 1mm in a unit second.

This property of a conductor to resist the flow of charge through it is called resistance.

SI unit :

Its SI unit is ohm, represented by the Greek letter Ω.

Definition of 1Ω: 

If the potential difference across the two ends of a conductor is 1 V and the current through it is 1 A, then the resistance R, of the conductor is 1 Ω. That is,
\[R=\frac{V}{I}\]
\[1\;ohm=\frac{1\;volt}{1\;ampere}\]
\[\textrm{or }1\;Ω=\frac{1\;V}{1\;A}\]

Relation between current and resistance: 

According to Ohm’s Law, 

\[I=\frac{V}{R}\]

the current through a resistor is inversely proportional to its resistance. If the resistance is doubled the current gets halved.

Since I is inversely proportional to the resistance of the circuit for a given V, we use this concept in controlling the amount of current in a domestic circuit by using a variable resistors.

Application of varying resistance: 

In many cases it is necessary to increase or decrease the current in an electric circuit like in case of an electric fan regulator and in electric iron for changing the amount of heat produced. The device used to control current without changing the voltage is called variable resistance.

 Symbol of variable Resistance:

Symbol of Rheostat ( a variable resistor):

Resistance of different material is different: 

The motion of electrons in an electric circuit constitutes an electric current. The electrons, however, are not completely free to move within a conductor. They are restrained by the attraction of the atoms among which they move. Thus, motion of electrons through a conductor is retarded by its resistance.

• A component of a given size that offers a low resistance is a good conductor.
• A conductor having some appreciable resistance is called a resistor.
• A component of identical size that offers a higher resistance is a poor conductor.
• An insulator of the same size offers even higher resistance.

Factors on which the resistance of a conductor depends: 

Resistance of the conductor is 

(i) Directly proportional to its length, 

(ii) Inversely proportional to its area of cross-section, and 

(iii) On the nature of its material. 

That is, 

\[R∝l ----(1)\]

\[R∝\frac{1}{A}----(2)\]

Combining (1) and (2)

\[R∝\frac{l}{A}\]

Or

\[R∝ρ\frac{l}{A}\]

Where ρ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor. 

Resistivity of a given material is independent of the dimension (i.e. length and area of cross-section) of given material and it depends only on nature of material and temperature. 

SI unit of resistivity: 

The SI unit of resistivity is Ω m. It is a characteristic property of the material.

Remarks: 

(1) The metals and alloys have very low resistivity in the range of 

\[10^{-8}ᘯ\;m\quad\textrm{to}\quad 10^{-6}ᘯ\;m\]

They are good conductors of electricity.

(2) Insulators like rubber and glass have resistivity of the order of

\[10^{12}ᘯ\;m\quad\textrm{to}\quad 10^{17}ᘯ\;m\]

(3) Both the resistance and resistivity of a material vary with temperature.

(4) Resistivity of a material does not change on changing the length and area of cross-section of the conductor.

(5) Resistivity of an alloy is generally higher than that of its constituent metals.

(6) Alloys are used in electrical heating devices, like electric iron, toasters etc because they do not oxidise (burn) readily at high temperatures.

(7) Tungsten is used almost exclusively for filaments of electric bulbs, because it does not melt at higher temperature, have high resistivity and can be easily drawn in to thin wires. 

(8) Copper and aluminium are generally used for electrical transmission lines because of their low resistivity they behave as a good conductor of electricity.

NOW CHECK YOUR PROGRESS!!!

1. A wire of given material having length l and area of cross-section A has a resistance of 4 Ω. What would be the resistance of another wire of the same material having length l/2 and area of cross-section 2A?

2. A wire of resistance 20 Ω is stretched to double its length. What will be its new (i) resistivity (ii) resistance?

3. On what factors does the resistance of a conductor depend?

4. Define the SI unit of resistance.

5. Why is the tungsten used almost exclusively for filament of electric lamps?

6. Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made of an alloy rather than a pure metal?

7. How does the resistance of a wire vary with its area of cross-section?

8. Why copper and aluminium wires are usually employed for electricity transmission?

9. Give two examples of materials which are (i) good conductor (ii) resistor (iii) insulator (iv) poor conductor.

10. Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why?

11. Why do electricians wear rubber hand-gloves while working with electricity?

12. Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal?

13. Name the device used to change resistance in a circuit to regulate current without changing the voltage source.

14. What is nichrome? State its one property and one use.

15. On what factor does the resistivity of a material depends?

Electric Potential

ELECTRIC POTENTIAL 

The movement of electrons in a metal wire takes place only if there is some sort of difference in electric pressure – called the potential difference – along the conductor. This difference of potential may be produced by a battery. The chemical action within a cell generates the potential difference across the terminals of the cell, even when no current is drawn from it. When the cell is connected to a conductor, the potential difference sets the charges in motion in the conductor and produces an electric current. 

Definition of Electric Potential: 

We define the electric potential difference between two points in an electric circuit as the work done to move a unit charge from one point to the other. 

Formula:

\begin{equation} \textit{ Potential difference between two points}  = \frac{work\ done}{charge} \end{equation}

Or in terms of symbols, we can write

\[V=\frac{W}{Q}\]

SI unit: 

The SI unit of electric potential difference is volt (V), named after Alessandro Volta. 

Definition of one volt: 

One volt is the potential difference between two points when 1 joule of work is done to move a charge of 1 coulomb from one point to the other. 
Therefore, 

\[1 volt=\frac{1 joule}{1 coulomb}\]

Device used to measure potential difference: 

The potential difference is measured by means of an instrument called the voltmeter.

Symbol in an electric circuit:

Connection: 

The voltmeter is always connected in parallel across the points between which the potential difference is to be measured. 

NOW CHECK YOUR PROGRESS!!! 

1. Name a device that helps to maintain potential difference across a conductor. 

2. What is meant by saying that potential difference between two points is 1V? 

3. Write the relation which states the relation between potential difference and work done. 

4. How much energy is given to each coulomb of charge passing through a 6V battery?

5. How much work is done in moving a charge of 2 C across two points having a potential difference of 12 V? 

6. Name the device that measures the potential difference across two points in an electric circuit. How it is connected in an electric circuit? 

MCQ on magnetic effect

MAGNETIC EFFECTS OF ELECTRIC CURRENT

Multiple Choice Questions

1. Choose the incorrect statement from the following regarding magnetic lines of field

(a) The direction of magnetic field at a point is taken to be the direction in which the north pole of a magnetic compass needle points

(b) Magnetic field lines are closed curves

(c) If magnetic field lines are parallel and equidistant, they represent zero field strength

(d) Relative strength of magnetic field is shown by the degree of closeness of the field lines

2. If the key in the arrangement is taken out (the circuit is made open) and magnetic field lines are drawn over the horizontal plane ABCD, the lines are

 

 (a) concentric circles

(b) elliptical in shape

(c) straight lines parallel to each other

(d) concentric circles near the point O but of elliptical shapes as we go away from it

3. A circular loop placed in a plane perpendicular to the plane of paper carries a current when the key is ON. The current as seen from points A and B (in the plane of paper and on the axis of the coil) is anti clockwise and clockwise respectively. The magnetic field lines point from B to A. The N-pole of the resultant magnet is on the face close to

(a) A

(b) B
(c) A if the current is small, and B if the current is large

(d) B if the current is small and A if the current is large

4. For a current in a long straight solenoid N- and S-poles are created at the two ends. Among the following statements, the incorrect statement is

(a) The field lines inside the solenoid are in the form of straight lines which indicates that the magnetic field is the same at all points inside the solenoid

(b) The strong magnetic field produced inside the solenoid can be used to magnetise a piece of magnetic material like soft iron, when placed inside the coil

(c) The pattern of the magnetic field associated with the solenoid is different from the pattern of the magnetic field around a bar magnet

(d) The N- and S-poles exchange position when the direction of current through the solenoid is reversed

6. Commercial electric motors do not use

(a) an electromagnet to rotate the armature

(b) effectively large number of turns of conducting wire in the current carrying coil

(c) a permanent magnet to rotate the armature

(d) a soft iron core on which the coil is wound

5. A uniform magnetic field exists in the plane of paper pointing from left to right as shown in Figure. In the field an electron and a proton move as shown. The electron and the proton experience

(a) forces both pointing into the plane of paper

(b) forces both pointing out of the plane of paper

(c) forces pointing into the plane of paper and out of the plane of paper, respectively

(d) force pointing opposite and along the direction of the uniform magnetic field respectively

7. In the arrangement shown in there are two coils wound on a non-conducting cylindrical rod. Initially the key is not inserted. Then the key is inserted and later removed. Then

(a) the deflection in the galvanometer remains zero throughout

(b) there is a momentary deflection in the galvanometer but it dies out shortly and there is no effect when the key is removed

 (c) there are momentary galvanometer deflections that die out shortly; the deflections are in the same direction

(d) there are momentary galvanometer deflections that die out shortly; the deflections are in opposite directions

8. Choose the incorrect statement

(a) Fleming’s right-hand rule is a simple rule to know the direction of induced current

(b) The right-hand thumb rule is used to find the direction of magnetic fields due to current carrying conductors

(c) The difference between the direct and alternating currents is that the direct current always flows in one direction, whereas the alternating current reverses its direction periodically

(d) In India, the AC changes direction after every 150 second

9. A constant current flows in a horizontal wire in the plane of the paper from east to west as shown in figure. The direction of magnetic field at a point will be North to South

(a) directly above the wire

(b) directly below the wire

(c) at a point located in the plane of the paper, on the north side of the wire

(d) at a point located in the plane of the paper, on the south side of the wire

10. The strength of magnetic field inside a long current carrying straight solenoid is

(a) more at the ends than at the centre

(b) minimum in the middle

(c) same at all points

(d) found to increase from one end to the other

11. To convert an AC generator into DC generator

(a) split-ring type commutator must be used

(b) slip rings and brushes must be used

(c) a stronger magnetic field has to be used

(d) a rectangular wire loop has to be used

12. The most important safety method used for protecting home

appliances from short circuiting or overloading is

(a) earthing

(b) use of fuse

(c) use of stabilizers

(d) use of electric meter

Physics sample Paper 2

        1.  The voltage – current (V – I) graph of a metallic conductor at two different temperature T1 and T2 is shown below. At which temperature is the resistance higher?

 

2. In the circuit diagram shown, the two resistance wires A and B are if same area of cross section and same material, but A is longer than B. Which ammeter A1 or A2 will indicate higher for current? Give reason.

 3. A student while studying the force experienced by a current carrying conductor in a magnetic field records the following observations.
(i)       The force experienced by the conductor increases as the current is increased.
(ii)      The force experienced by the conductor decreases as the strength of the magnetic field is increased.
Which of the two observation is correct and why?

4.  How would the reading of voltmeter (V) change if it is connected between B and C? Justify your answer.

  

5.  What would be the reading of ammeter and voltmeter in the given circuit?

6.  Two conducting wires of same material, equal length and equal diameter are first connected in series and then in parallel. Compare the equivalent resistance in two cases.

7.  What change in the deflection of the compass needle placed at a point near current carrying straight conductor shall be observed if the –
(a)    Current through the conductor is increased?
(b)    Direction of current in the conductor is reversed?
(c)    Compass is moved away from the conductor?

8.  What are magnetic field lines? List any two characteristics of field lines. Draw the pattern of magnetic field of lines due to a current carrying circular loop.

9.  Draw the schematic diagram showing common domestic circuit.

10. State the function of an earth wire? Why is it necessary to earth metallic appliances such as an electric iron?

Physics sample paper 1

SAMPLE QUESTION PAPER 1

1. You have two metallic wires of resistances 6 ohms and 3 ohms. How will you connect these wires to get the effective resistance of 2 ohms? 

2. Calculate the electrical energy consumed by a 1200 W toaster in 20 minutes.

3. State Ohm's Law. Write a mathematical expression for it.

4. No two magnetic field lines interest each other. Explain.

5. What precautions should be taken to avoid the overloading of domestic electric circuits?

6. An electric oven of 2KW power rating is operated in a domestic electric circuit (220V), that has a current rating 5 A. What result do you expect? Explain.

7. A piece of wire of resistance 20 ohms is drawn out so that its length is increased to twice its original length. Calculate the resistance of the wire in the new situation.

8. Study the following circuit and answer the following questions.

   (i) State the type of combination of the two resistors in the circuit.
   (ii) How much current is flowing through
      (a) 10 ohms and through
      (b) 15 ohms resistors
   (iii) What is ammeter reading?

9. A positively charged particle projected towards west is deflected towards north by a magnetic field. What is the direction of the magnetic field?

10. Draw the magnetic field lines of the field produced due to a current carrying circular loop.

11. State the law used to find the direction of magnetic field around a straight current carrying conductor.

12. (a) What is a solenoid?
      (b) Draw the field lines of the magnetic field through and around a current carrying solenoid.
      (c) Which rule helps to find the force on a current carrying conductor in a magnetic field? State the rule.

MCQs on Physics Practicals

MULTIPLE CHOICE QUESTIONS

1. A cell, a resistor, a key and ammeter are arranged as shown in the circuit diagrams. The current recorded in the ammeter will be

(a) maximum in (i)
(b) maximum in (ii)
(c) maximum in (iii)
(d) the same in all the cases

2. In the following circuits, heat produced in the resistor or combination of resistors connected to a 12 V battery will be

(a) same in all the cases
(b) minimum in case (i)
(c) maximum in case (ii)
(d) maximum in case (iii)

3. Electrical resistivity of a given metallic wire depends upon
(a) its length
(b) its thickness
(c) its shape
(d) nature of the material

4. A current of 1 A is drawn by a filament of an electric bulb. Number of electrons passing through a cross section of the filament in 16 seconds would be roughly
(a) 10 raise to the power 20
(b) 10 raise to the power 16
(c) 10 raise to the power 18
(d) 10 raise to the power 23

5. Which of the circuit components in the following circuit diagrtam are connected in parallel?

   (a)    R1 and R2 only

   (b)   R2 and V only

   (c)   R1 and V only

   (d)   R1, R2 and V

6. The readings of the current flowing through a conductor and the potential difference across its two ends are shown in the ammeter and voltmeter given below. The resistance of the conductor would be

 (a)    20 ohms

 (b)   5.0 ohms

 (c)    2.0 ohms

 (d)   0.2 ohms

7. To determine the equivalent resistance of a series combination of two resistors R1 and R2, a student arrange the following set up.

Which of the following statements will be true for this circuit? It gives

(a)    Incorrect reading for current I and potential difference V both.

(b)   Correct reading for current I, but incorrect reading for potential difference V.

(c)    Correct reading for potential difference V but incorrect reading for current I

(d)   Correct reading for both V and I

8. What will happen to the current passing through a conductor if potential difference across it is doubled and the resistance is halved?
(a)    Remains unchanged
(b)   Becomes double
(c)    Becomes halved
(d)   Becomes four times

9. In the experiment to study the dependence of current on potential difference across a resistor, a student obtained a graph as shown in the diagram.

The value of resistance of the resistor is

(a)    0.1 ohms

(b)   1.0 ohms

(c)    10 ohms

(d)   100 ohms

10. For the circuits shown in figure I and II the ammeter reading would be:

(a)    1 A in circuit I and 0 A in circuit II
(b)   0 A in both circuits
(c)    1 A in both circuits
(d)   0 A in circuit I and 1 A in circuit II