**Question and answer**

**Question and answer**

** on **

**on**

**Electric Current**

**Electric Current**

**The theory of this topic:**

Class 12, Physics Tutorials, Module – 02, Chapter – 01, Electric Current

**For 1 marks :**

**1 ) Name the constant physical quantity related to Ohm’s law.**

Ans : Temperature of the conductor and other physical condition.

**2 ) What will be the resistance of the conductor, if its cross-sectional area is halved while its length remains unchanged?**

Ans : If the cross-sectional area of the conductor is halved, its resistance becomes twice.

**3 ) Name any one factor on which internal resistance depends?**

Ans : Nature of the electrolytes

**4 ) What will be the expression for the internal resistance of the cell if it is discharging?**

Ans : ir = E – V

**5 ) What will be the expression for the internal resistance of the cell if it is charging?**

Ans : ir = E + V

**6 ) What is the positive temperature coefficient?**

Ans : If the resistance increases with the increase in temperature by unity, then the temperature coefficient is called positive temperature coeffiecient.

**7 ) What is the negative temperature coefficient?**

Ans : If the resistance decreases with the increase in temperature by unity, then the temperature coefficient is called negative temperature coeffiecient.

**8 ) What is the nature of the temperature coefficient of the good conductor?**

Ans : Positive

**9 ) What is the nature of the temperature coefficient of the semiconductor?**

Ans : Negative

**10 ) How electric current varies with potential difference across the ends of the conductor?**

Ans : Directly varies

**11 ) Draw the graph for the non-ohmic conductor.**

Ans :

**12 ) What is relaxation time?**

Ans : The relaxation time is defined as the time during which two successive collision occured.

**13 ) What is the drift velocity of the electron moving under the influence of the electric field E and relaxation time is τ? **

Ans : *v _{d}* = ( e E / m ) τ

wher ‘ m ‘ is the electronic mass, ‘ e ‘ is the electronic charge.

**14 ) What will be the effect on the electric current flowing through the conductor if the drift velocity becomes twice?**

Ans : The electric current also become twice.

**15 ) What will be the equivalent resistance of the parallel combination of two equal resistors?**

Ans : The equivalent resistance of the parallel combination of two equal resistors is half of the resistance of each resistor that is’

R_{p} = R / 2

**16 ) What is the SI – unit of electron mobility? **

Ans : ms^{-1}N^{-1}C

**For 2 or 3 marks :**

**1 ) What are the factors influencing the internal resistance of the cell?**

Ans : Internal resistance of the cell depends on the following factors :

- distance between two plates
- nature of electrolytes
- nature of nature of electrodes
- area of plates
- the concentration of the electrolytes

**2 ) Establish the expression for the internal resistance of the cell? **

Ans :

Following the circuit,

r = internal resistance

R = external resistance

E = E.M.F of the cell

V = voltage drop across R = iR

i = current flowing throgh the circuit = emf of the battery / total resistance of the ciruit

i = E / ( R + r )

⇒ iR + ir = E

⇒ V + ir = E

**⇒ ir = E – V ——————————————— ( A )**

⇒ **r = ( E – V ) / i ———————————– ( 1 ) **

∵ i = V / R, putting this value of i in the above eqaution, we get

r = ( E – V ) / ( V / R )

⇒ r = ( E / V – V / V ) R

**⇒ r = ( E / V – 1 ) R ————————————- ( 2 ) **

**3 ) What is the relation between the electric current and drift velocity?**

Ans :

let

*l* = length of the conductor

A = cross sectional area of the conductor

V = potential differnce across the two ends of the conductor.

n = number of the free electrons per unit volume

N = total number of free electrons = n * volume of the conductor = nA*l*

All free electrons move randomly before applying any electric field. When the electric field is applied to the conductor , all the electrons arrnaged and move in a specific direction and constitutues electric current flowing in opposite direction of the electorn. This electric current is nothing but the drift velocity.

Let I = electric current flowing through the conductor

I = total charge / t

I = Ne / t

I = nA*le / t*

I = neA ( *l* / t )

**I = neA v_{d}**

**4 ) What is the relation between the electric current flowing through the electric conductor and the applied electric field?**

Ans :

Let v_{1} , v_{2} , v_{3} …………… are the final velocity of the electrons movign under the influence of applied electirc field E. τ is the relaxation time between two succesive colission of electrons when electric current flows ‘n’ ihe electron density.

*v _{d}* = ( v

_{1}+ v

_{2}+ v

_{3}+ ………………… ) / n

*v _{d}* = { ( u

_{1}+ aτ

_{1}) + ( u

_{1}+ aτ

_{2}) + ………………………. } / n

*v _{d }*= { ( u

_{1}+ u

_{2}+ …………….. ) / n } + { a ( τ

_{1}+ τ

_{2}+ ……………….. ) / n } —————- ( 1 )

Before applying electirc field, the average velocity is zero as all electrons move randomly and effect produced by these electrons are canclled by each other.

therfore,

( u_{1} + u_{2} + …………….. ) / n = 0

and we Know that force experineced by each electron is given by

F = e E

ma = eE

a = eE / m

and ( τ_{1} + τ_{2} + ……………….. ) / n = τ = average relaxation time

where, a is the acceleration produced by each electron, m is the mass of the electorn, E is the applied electric field.

Now, putting the value of ‘a ‘ in equaion ( 1 ), we get

*v _{d}* = 0 + eEτ / m

*v _{d}* = ( e E / m ) τ

**5 ) Define the term electron mobility? **

Ans : The drift velocity of free electrons per unit electric field is called the electron mobility.

**6 ) What is the relation between the electron mobility and relaxation time?**

Ans : Electron mobility ( μ ) = drift velocity / electric field

μ = ( eEτ / m ) / E

μ = eτ / m

where e is the electronic charge, m is the electronic mass.

**7 ) What is the relation between the electron mobility and electric current? **

Ans : We know that,

I = neA*v _{d}*

I = neA ( eEτ / m )

I = neAE ( eτ / m )

I = neAEμ

where n = electron density

e = electronic charge

A = cross-sectional area

E = Electric field

μ = Electron mobility

**8 ) Define the current density? **

Ans : The quantity of the electric current flowing per unit cross-sectional area of the conductor is called current density.

**9 ) What is the relation between the current density and electron mobility?**

Ans : We know that,

I = neA*v _{d}*

and current density is given by

J = I / A

J = ( neA*v _{d}* ) / A

J = ne*v _{d}*

J = ne ( eEτ / m ) [ *v _{d }*= eEτ / m ]

J = neE ( eτ / m )

J = neEμ

**10 ) What is the relation between the current density and the relaxation time?**

Ans :

We know that,

I = neA*v _{d}*

and current density is given by

J = I / A

J = ( neA*v _{d}* ) / A

J = ne*v _{d}*

J = ne ( eEτ / m ) [ *v _{d }*= eEτ / m ]

J = ne^{2}Eτ / m

**11 ) Show that the resistance of parallel combination of resistors is less than the individual resistance.**

Ans :Let the equivalent resistance of the parallel combination of the n resistors is R_{p}

1 / R_{p} = 1 / R_{1} + 1 / R_{2} + 1 / R_{3} + ……………………… + 1 / R_{n}

For two different resistors,

1 / R_{p} = 1 / R_{1} + 1 / R_{2}

R_{p} = R_{1}R_{2} / ( R_{1} + R_{2} )

1 / R_{p} = 1 / R_{1} + 1 / R_{2}

R_{p} / R_{1} = R_{2} / ( R_{1} + R_{2} ) < 1

R_{p} < R_{1}

Hence, we can see that the equivalent resitance of the parallel combination of the resistors is always less than the individual one.

**12 ) Show that the resistance of series combination of resistors is greater than the individual resistors.**

Ans : Let the n resistors are connected in series combination. The equivalent resistance is given by

R_{s} = R_{1} + R_{2} + R_{3} + ……………………… + R_{n}

( R_{2} + R_{3} + ……………………… + R_{n} ) is a positive quantity

Hence,

R_{s} = R_{1} + Positive quantity

R_{s} > R_{1}

Thus the resistance of the series combination of the resistors is greater than the individual.

**13 ) What is voltmeter? How it is connected in an electronic circuit ? **

Ans : A voltmeter is an electronic device used for measuring the voltage in an electric circuit. It is connected in parallel in a circuit as it has high internal resistance.

**14 ) Define ammeter. How the resistance is connected with the ammeter in an electric circuit?**

Ans : An ammeter is an electronic device used for measuring the electric current in the electronic circuit. It is always connected in series as it has very low internal resistance.