Current Electricity Test

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Current Electricity Test - 25

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Question 1
1 / -0

Electromotive force of a battery represents

A
force

B
energy

C
electric potential energy per unit charge

D
current

Solution

When a voltage is generated by a battery, this generated voltage has been traditionally called an electromotive force or emf. The emf represents electric potential energy per unit charge (voltage) which has been made available to free electrons by the generating mechanism and is not a force.

The term emf is useful to distinguish voltage generated by the battery from those which occur in a circuit as a result of energy dissipation( Like Voltage drop across a resistor ) .
Question 2
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In a meter bridge, a standard resistor of R ohm is connected in the left gap and two wires A and B are connected one after the other in the right gap. The balancing length measured from the left is 50 cm for either of them. If the two wires are connected is series and put in the right gap, the balancing length measured from the left would be (in cm)

A
25

B
33.3

C
66.7

D
75

Solution

let the resistance of wire A be a and that of wire B and b,then
$$\dfrac{R}{50}=\dfrac{a}{100-50}$$$$\therefore$$ a$$=R$$
also,$$\dfrac{R}{50}=\dfrac{b}{100-50}$$ $$\therefore$$ b$$=R$$
when both are connected in series$$\dfrac{R}{i}=\dfrac{2a}{100-i}$$
or $$100-i= \ 2i$$
or $$i=\dfrac{100}{3}$$
Question 3
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The resistivity of a wire varies with its

A
length

B
cross-section

C
mass

D
material

Solution

Resistivity is the property of the material. It doesn't depend upon its length or area.
Question 4
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Which of the following quantities do not change when a resistor connected to a battery is heated due to the current?

A
Drift speed

B
Resistivity

C
Resistance

D
Number of free electrons

Solution

Resistance, resistivity and drift velocity varies with relaxation time which is dependent on temperature.
Number of free electrons in a conductor remains invariant even if its temperature changes.Hence correct option is option D.
Question 5
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As the temperature of a conductor increases, its resistivity and conductivity change. The ratio of resistivity to conductivity

A
increases

B
decreases

C
remains constant

D
may increase or decrease depending on the actual temperature

Solution

The resistivity of a conductor is given by
$$\rho = \dfrac{m}{ne^2\tau}$$

where, $$m$$ is mass of an electron, $$e$$ is charge on electron, $$n$$ is number of free electrons per unit volume in conductor and $$\tau$$ is relaxation time.

$$\Rightarrow \rho \propto \dfrac{1}{\tau}$$ ...............................(1)
Also, the conductivity is reciprocal of resistivity i.e.
$$\sigma = \dfrac{1}{\rho}$$ ...............................................................(2)
$$\Rightarrow \sigma \propto \tau$$ .............(3)............from ( 1 )and ( 2 )

$$\dfrac{\rho}{\sigma} \propto \dfrac{1}{\tau^2}$$ ..............from (1) and (3)

When temperature increases relaxation time will decrease and hence, ratio of resistivity and conductivity will increase.
Question 6
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Which of the following wiring diagrams could be experimentally determine $$R$$ using ohms law? Assume an ideal voltmeter and an ideal ammeter

A

B

C

D

Solution

Ohm's law states that current through the conductor between two points is directly proportional to the potential difference across the two points.
Which can be represented by circuit diagram as below.
Question 7
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The amount of work done by the cell on a unit positive charge carrier to force it to go to the point of higher potential is called

A
power

B
voltage

C
emf

D
energy

Solution

The rate at which energy is drawn from a source of energy when unit current flows through the circuit or device is called emf. It is measured in volts.
Question 8
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e.m.f. is measured in

A
$$\text{Joules}$$

B
$$\dfrac{\text{Joules}}{\text{coulomb}}$$

C
$$\text{Joule-coulombs}$$

D
$$\dfrac{\text{coulomb}}{\text{Joules}}$$

Solution

$$Volt\quad =\dfrac { W }{ Q } =\dfrac { joule }{ Coulomb } $$
The emf of a cell is the open circuit potential difference across it's ends.
So it has the unit of volt or joule per coulomb.
Question 9
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The current in a wire is doubled keeping temperature constant. Which of the following statements is/are wrong?

A
The current density is doubled

B
The conduction electron density is doubled

C
The mean time between collisions is constant

D
The electron drift speed is doubled

Solution

Here, the current $$I$$, in a wire is doubled keeping temperature constant. Hence the current density $$J$$, will also be doubled since, $$J = \dfrac {I}{\text {Area}}$$.
Also, the drift velocity $$V_d$$, will also be doubled since, $$I = neAV_d$$
The mean time between collisions is constant since it is independent of current.
And, the number of electrons per unit volume in a conductor remains invariant for change in current.
Question 10
1 / -0

In the absence of an electric field, the mean velocity of free electrons in a conductor at absolute temperature $$(T)$$ is

A
$$zero$$

B
independent of $$T$$

C
proportional to $$T$$

D
proportional to $$T^2$$

Solution

In the absence of electric field, the electron moves in zig-zag direction as shown in figure. So net displacement is zero, hence mean velocity of free electrons in a conductor at absolute temperature is zero