# 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 : vd = ( 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’

Rp = R / 2

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

Ans : ms-1N-1C

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 = nAl

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 = nAle / t

I = neA ( l / t )

I = neAvd

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

Ans : Let v1 , v2 , v3 …………… 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.

vd = ( v1 + v2 + v3 + ………………… ) / n

vd = { ( u1 + aτ1 ) + ( u1 + aτ2 ) + ………………………. } / n

vd = { ( u1 + u2 + …………….. ) / n } + { a ( τ1 + τ2 + ……………….. ) / 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,

( u1 + u2 + …………….. ) / n = 0

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

F = e E

ma = eE

a = eE / m

and ( τ1 + τ2 + ……………….. ) / 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

vd = 0 + eEτ / m

vd = ( 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 = neAvd

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 = neAvd

and current density is given by

J = I / A

J = ( neAvd ) / A

J = nevd

J = ne ( eEτ / m )                            [ vd = 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 = neAvd

and current density is given by

J = I / A

J = ( neAvd ) / A

J = nevd

J = ne ( eEτ / m )                            [ vd = eEτ / m ]

J = ne2Eτ / 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 Rp

1 / Rp = 1 / R1 + 1 / R2 + 1 / R3 + ……………………… + 1 / Rn

For two different resistors,

1 / Rp = 1 / R1 + 1 / R2

Rp = R1R2 / ( R1 + R2 )

1 / Rp = 1 / R1 + 1 / R2

Rp / R1 = R2 / ( R1 + R2 ) < 1

Rp < R1

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

Rs = R1 + R2 + R3 + ……………………… + Rn

( R2 + R3 + ……………………… + Rn ) is a positive quantity

Hence,

Rs = R1 + Positive quantity

Rs > R1

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.