Is electric current a vector or scalar quantity? Explain.

1

(a)

Electric current is a scalar quantity because it does not follow the laws of vectors addition, i.e., the angle between the wires carrying the current does not affect the total current in the circuit.

A steady current is flowing in a cylindrical conductor. Is there any electric field within the conductor?

1

(a)

Yes. A steady current in a cylindrical conductor if electric force is acting on free electrons which make the electrons to move in a particular direction. It is possible due to electric field within the conductor.

Define the term 'drift velocity' of charge carriers in a conductor and write its relationship with the current flowing through it.

1

(a)

Drift velocity is the average velocity with which the free electrons get drifted towards the positive end of the conductor under the influence of an external electric field applied.
The relation between current I and drift velocity v_d is I = nAev_d
Where n is the number density of electrons in a conductor of area of cross-section A and e is the charge on an electron. 

The specific resistance of copper, silver and constantan are 1.78 x 10^-6 Ω-cm, 10^-6 Ω-cm and 48 x 10^-6 Ω-cm, respectively. Which is the best conductor and why?

1

(a)

The best conductor is silver because electrical conductivity is inversely proportional to the resistivity and resistivity of silver is least.

Is the formula V = IR true for non-ohmic devices also?

1

(a)

Yes, the formula defines resistance R = V/I and not Ohm's law, for which, \(\frac{V}{I}=R= constant.\) 

Two wires of equal length one of copper and other of manganin have the same resistance. Which wire is thicker?

1

(a)

\(R=\rho\ l/A \ or \ A \propto \rho\) 
if l and R are constant. Since \(\rho\) is greater for manganin than for copper, hence manganin wire is thicker than copper wire.

If potential difference V applied across a conductor is increased by 2 V, how will the drift velocity of the electrons change?

1

(a)

Ler R is the resistance of the conductor. In the first case, current in a conductor, I = V/R.
In second case current in conductor,
\(I'=\frac{2V+V}{R}=\frac{3V}{R}=3I\)
\(As \ \ I = nAev_d \ \ or \ \ v_d \propto I\)  (\(\because n, A, e \ \ are \ \ constant)\)
\(\therefore \frac{v_d'}{v_d}=\frac{I'}{I}=\frac{3I}{I}=3 \ or \ v_d'=3v_d\)
It means drift velocity becomes tripled.

Explain why resistance becomes less in parallel combination.

1

(a)

In a parallel combination of resistors, the effective area of a cross-section of the conductor increases. As \(R \propto l\), therefore, resistance decreases.

Is it possible that there is no potential difference between the plates of a cell? If yes, under what condition?

1

(a)

When a cell is short-circuited, it gets totally discharged. The potential difference between the two plates of the cell becomes zero.

What are two practical forms of Wheatstone bridge?

1

(a)

Slide wire bridge and post office box.

The emf of the driving cell used in the main circuit of the potentiometer should be more than the potential difference to be measured. Why?

1

(a)

If it is not so, then the balance point will not be obtained on the potentiometer wire.

Whether electric field inside potentiometer wire is constant or variable?

1

(a)

Electric field intensity E = V/l = a constant.

What is the material of the element used in an electric heater?

1

(a)

Nichrome

Is the motion of a change across junction momentum conserving? Why or why not?

1

(a)

When an electron approaches a junction, in addition to the uniform electric field E facing it normally, it keeps the drift velocity fixed. as drift velocity depends on E by the relation of drift velocity, \({ v }_{ d }=\frac { eE\tau }{ m } \) This results into accumulation of changes on the surface of wires at the junction. These produce an additional electric field. These fields change the direction conserving momentum. Thus, the motion of a charge junction is not momentum conserving.

Two wires of equal length, one of copper and the other of manganin have the same resistance. Which wire is thicker?

1

(a)

Nichrome wire having more resistivity (p) will heat up more, as heat produced \(=I^{2} R=I^{2} \rho \frac{l}{A}\)

State the underlying principle of a potentiometer.

1

(a)

When a constant current flows through a wire, the potential difference, between any two points on the wire of uniform cross section, is directly proportional to the length of the wire between these points,
Alternatively:
\(V\ a\ l\ or\ /\ dl\)=constant

Why is adsorption always exothermic?

1

(a)

In adsorption there is a decrease in residual forces of the surface which evolves as heat. Hence it is exothermic in nature.

A wire of resistance 8R is bent in the form of a circle. What is the effective resistance between the ends of a diameter AB?

1

(a)

The resistance of the whole wire is 8Ω, which is bent in the form of a circle. We have to find the effective resistance between the ends of diameter AB. Diameter of the circle divides the circle into two equal parts. The resistance of each such part will be 8/2=4Ω
(Resistance R ∝ length of wire l, if length is halved then resistance will also become half). From the figure, it is clear that both the parts are in parallel combination. So, effective resistance between A and B is given by
\(\frac { 1 }{ { R }_{ AB } } =\frac { 1 }{ { R }_{ 1 } } +\frac { 1 }{ { R }_{ 2 } } \)
⇒ \(\frac { 1 }{ { R }_{ AB } } =\frac { 1 }{ 4 } +\frac { 1 }{ 4 } \)

⇒ \({ R }_{ AB }=\frac { a }{ 1+1 } \)=2Ω
R_effective = 2R

Plot a graph showing variation of current versus voltage for the material GaAs.

1

(a)

Variation of current versus voltage for the material GaAs.

Define the term electrical conductivity of a metallic wire. Write its SI unit.

1

(a)

The electrical conductivity (σ) of a metallic wire is defined as the ratio of the current density to the electric field it creates. Its SI unit is mho per meter (Ω^-1/m)

Write a relation between current and drift velocity of electrons in a conductor. Use this relation to explain how the resistance of a conductor changes with the rise in temperature?

1

(a)

Relation between current and drift velocity of electrons in a conductor is given by
I=Anev_d
where, I = current,
A = area of conductor,
n = number density of electrons and
v_d = drift velocity.
with the increase in temperature of a metallic conductor, resistance increases and hence, drift velocity decreases.

Plot a graph showing the variation of resistance of a conducting wire as a function of its radius. Keeping the length of the wire and its temperature as constant.

1

(a)

Resistance of a conductor of length I and radius r is given by
R=\(\rho \frac { 1 }{ { \pi r }^{ 2 } } \)

Two materials Si and Cu, are cooled from 300 K to 60 K. What will be the effect on their resistivity?

1

(a)

In silicon, the resistivity increases with decrease in temperature.
In copper, the resistivity decreases with decrease in temperature.

The three coloured bands, on a carbon resistor are red, green and yellow, respectively. Write the value of its resistance.

1

(a)

According to the colour code of resistances. Code for red = 2, Code for green = Sand Code for yellow = 4
∴ Resistance of the wire = 25 x 10⁴Ω ± 20%

A cell of emf E and internal resistance r draws a current I. Write the relation between terminal voltage V in terms of E, I and r.

1

(a)

When a current I draws from a cell of emf E and internal resistance r, then the terminal voltage
V = E - lr

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.

1

(a)

Reduced by half

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

1

(a)

Increasing in heat

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

1

(a)

Parallel (i.e)R

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?

1

(a)

2:1

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

1

(a)

R