Additional Questions - Chapter 2 Current Electricity 12th Science Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On May 15, 2024

By SaraNextGen

Additional Questions Solved
I. Choose the Correct Answer
Question 1.
When current I flows through a wire, the drift velocity of the electrons is $\mathrm{v}$. When current 21 flows through another wire of the same material having double the length and area of cross-section, the drift velocity of the electrons will be-
(a) $\frac{v}{4}$
(b) $\frac{v}{2}$
(c) $\mathrm{v}$
(d) $2 \mathrm{~V}$
Answer:
(c) $\mathrm{v}$
Hint:
$
\mathrm{V}_{\mathrm{d}}=\frac{1}{n A e} ; \mathrm{v}^{\prime} \mathrm{d}=\frac{2 I}{(2 A) n e}=\mathrm{v}_{\mathrm{d}}
$
Question 2.
A copper wire of length $2 \mathrm{~m}$ and area of cross-section $1.7 \times 10^{-6} \mathrm{~m}^2$ has a resistance of $2 \times 10^{-2} \Omega$. The
resistivity of copper is
(a) $1.7 \times 10^{-8} \Omega \mathrm{m}$
(b) $1.9 \mathrm{x}^{-8} \Omega \mathrm{m}$
(c) $2.1 \times 10^{-7} \Omega \mathrm{m}$
(d) $2.3 \times 10^{-7} \Omega \mathrm{m}$
Answer:
(a) $1.7 \times 10^{-8} \Omega \mathrm{m}$
Hint:
Resistivity, $\rho=\frac{R A}{l}=\frac{2 \times 10^{-2} \times 1.7 \times 10^{-6}}{2}=1.7 \times 10^{-8} \Omega \mathrm{m}$
Question 3.
If the length of a wire is doubled and its cross-section is also doubled, then its resistance will
(a) become 4 times
(b) become $1 / 4$
(c) becomes 2 times
(d) remain unchanged
Answer:
(d) remain unchanged

Question 4.
A $10 \mathrm{~m}$ long wire of resistance $20 \Omega$ is connected in series with a battery of emf $3 \mathrm{~V}$ and a resistance of $10 \Omega$. The potential gradient along the wire in volt per meter is
(a) 6.02
(b) 0.1
(c) 0.2
(d) 1.2
Answer:
(c) 0.2
Hint:
Potential difference across the wire $=\frac{20}{3} \times 3=2 \mathrm{~V}$
Potential gradient $=\frac{v}{l}=\frac{2}{10}=0.2 \mathrm{~V} / \mathrm{m}$
Question 5.
The resistivity of a wire
(a) varies with its length
(b) varies with its mass
(c) varies with its cross-section
(d) does not depend on its length, cross-section and mass.
Answer:
(d) does not depend on its length, cross-section and mass.
Question 6.
The electric intensity E, current density and conductivity a are related as
(a) $\mathrm{j}=\sigma E$
(b) $\mathrm{j}=\frac{E}{\sigma}$
(c) $\mathrm{JE}=\mathrm{s}$
(d) $j=\sigma^2 E$
Answer:
(a) $j=\sigma E$

Question 7.
For which of the following dependences of drift velocity $V_d$ on electric field $E$, is Ohm's law obeyed?
(a) $v_d \propto E$
(b) $v_d \propto E^2$
(c) $v_{\mathrm{d}} \propto \sqrt{E}$
(d) $\mathrm{v}_{\mathrm{d}}=$ constant
Answer:
(a) $v_d \propto E$
Hint:
$
\mathrm{v}_{\mathrm{d}}=\frac{1}{n A e}=\frac{j}{n e}=\left(\frac{\sigma}{n e}\right) \mathrm{E} \Rightarrow \mathrm{v}_{\mathrm{d}} \propto \mathrm{E}
$
Question 8.
A cell has an emf of $1.5 \mathrm{~V}$. When short circuited, it gives a current of $3 \mathrm{~A}$. The internal resistance of the cell is .
(a) $0.5 \Omega$
(b) $2.0 \Omega$
(c) $4.5 \Omega$
(d) $\frac{1}{4.5} \Omega$
Answer:
(a) $0.5 \Omega$
Hint:
$
\mathrm{r}=\frac{\xi}{I}=\frac{1.5}{3}=0.5 \Omega \text {. }
$
Question 9.
The resistance, each of $1 \Omega$, are joined in parallel. Three such combinations are put in series. The resultant resistance is
(a) $9 \Omega$
(b) $3 \Omega$
(c) $1 \Omega$
(d) $\frac{1}{3} \Omega$
Answer:
(c) $1 \Omega$
Hint:
$
\begin{aligned}
& \mathrm{R}_{\mathrm{p}}=1+1+1=3 \Omega ; \\
& \frac{1}{R_s}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{3}{3}=1 \\
& \Rightarrow \mathrm{R}_{\mathrm{S}}=1 \Omega .
\end{aligned}
$

Question 10.
Constantan is used for making standard resistance because it has
(a) high resistivity
(b) low resistivity
(c) negligible temperature coefficient of resistance
(d) high melting point
Answer:
(c) negligible temperature coefficient of resistance
Question 11.
Kirchhoff's two laws for electrical circuits are magnifestations of the conservation of
(a) charge only
(b) both energy and momentum
(c) energy only
(d) both charge and energy
Answer:
(d) both charge and energy
Question 12.
The resistance $R_0$ and $R_t$ of a metallic wire at temperature $0^{\circ} \mathrm{C}$ and t ${ }^{\circ} \mathrm{C}$ are related as (a is the temperature co-efficient of resistance).
(a) $\mathrm{R}_{\mathrm{t}}=\mathrm{R}_0(1+\alpha \mathrm{t})$
(b) $R_t=R_0(1-\alpha t)$
(c) $\mathrm{R}_{\mathrm{t}}=\mathrm{R}_0(1+\alpha t)^2$
(d) $\mathrm{R}_{\mathrm{t}}=\mathrm{R}_0(1-\alpha \mathrm{t})^2$
Answer:
(a) $\mathrm{R}_{\mathrm{t}}=\mathrm{R}_0(1+\alpha \mathrm{t})$

Question 13.
A cell of emf $2 \mathrm{~V}$ and internal resistance $0.1 \Omega$ is connected with a resistance of $3.9 \Omega$. The voltage across the cell terminals will be
(a) $0.5 \mathrm{~V}$
(b) $1.9 \mathrm{~V}$
(c) $1.95 \mathrm{~V}$
(d) $2 \mathrm{~V}$
Answer:
(c) $1.95 \mathrm{~V}$
Hint:
$
\mathrm{V}=\frac{E R}{R+r}=\frac{2 x 3.9}{3.9+0.1}=1.95 \mathrm{~V}
$
Question 14.
A flow of $10^7$ electrons per second in a conduction wire constitutes a current of
(a) $1.6 \times 10^{-26} \mathrm{~A}$
(b) $1.6 \times 10^{12} \mathrm{~A}$
(c) $1.6 \times 10^{-12} \mathrm{~A}$
(d) $1.6 \times 10^{26} \mathrm{~A}$
Answer:
(c) $1.6 \times 10^{-12} \mathrm{~A}$
Hint:
$
\mathrm{I}=\frac{Q}{t}=\frac{10^7 \times 1.6 \times 10^{-19}}{1}=1.6 \times 10^{12} \mathrm{~A}
$
Question 15 .
Sensitivity of a potentiometer can be increased by

(a) increasing the emf of the cell
(b) increasing the length of the wire
(c) decreasing the length of the wire
(d) none of the above
Answer:
(b) increasing the length of the wire
Question 16.
Potential gradient is defined as
(a) fall of potential per unit length of the wire.
(b) fall of potential per unit area of the wire.
(c) fall of potential between two ends of the wire.
(d) none of the above.
Answer:
(a) fall of potential per unit length of the wire.
Question 17.
$\mathrm{n}$ equal resistors are first connected in series and then in parallel. The ratio of the equivalent resistance in two cases is
(a) $n$
(b) $\frac{1}{n^2}$
(c) $n^2$
(d) $\frac{1}{n}$
Answer:
(c) $n^2$
Hint:
Required ratio $=\frac{n \mathrm{R}}{\left(\frac{\mathrm{R}}{n}\right)}=\mathrm{n}(\mathrm{c}) \mathrm{n}^2$
Question 18.
A galvanometer is converted into an ammeter when we connect a
(a) high resistance in series
(b) high resistance in parallel
(c) low resistance in series
(d) low resistance in parallel
Answer:
(d) low resistance in parallel
Question 19.
The reciprocal of resistance is
(a) conductance
(b) resistivity
(c) conductivity
(d) none of the above

Answer:
(a) conductance
Question 20 .
A student has 10 resistors, each of resistance $r$. The minimum resistance that can be obtained by him using these resistors is
(a) $10 r$
(b) $\frac{r}{10}$
(c) $\frac{r}{100}$
(d) $\frac{r}{5}$
Answer:
(b) $\frac{r}{10}$
Question 21.
The drift velocity of electrons in a wire of radius $r$ is proportional to
(a) $\mathrm{r}$
(b) $r^2$
(c) $\mathrm{r}^3$
(d) none of the above
Answer:
(d) none of the above
Question 22.
Kirchhoff's first law, i.e. $\sum I=0$ at a junction deals with conservation of
(a) charge
(b) energy
(c) momentum
Answer:
(a) charge
Question 23.
The resistance of a material increases with temperature. It is a
(a) metal
(b) insulator
(c) semiconductor
(d) semi-metal
Answer:
(a) metal

Question 24.
Five cells, each of emf $E$, are joined in parallel. The total emf of the combination is
(a) $5 \mathrm{E}$
(b) $\frac{E}{5}$
(c) $\mathrm{E}$
(d) $\frac{5 E}{2}$
Answer:
(c) $\mathrm{E}$
Question 25.
A carbon resistance has colour bands in order yellow, brown, red. Its resistance is
(a) $41 \Omega$
(b) $41 \times 10^2 \Omega$
(c) $41 \times 10^3 \Omega$
(d) $4.2 \Omega$
Answer:
(b) $41 \times 10^2 \Omega$
Question 26.
The conductivity of a superconductor is
(a) infinite
(b) very large
(c) very small
(d) zero
Answer:
(a) infinite
Question 27.
The resistance of an ideal voltmeter is
(a) zero
(b) very high
(c) very low
(d) infinite
Answer:
(d) infinite

Question 28.
Carriers of electric current in superconductors are
(a) electrons
(b) photons
(c) holes
Answer:
(c) holes
Question 29.
Potentiometer measures potential more accurately because
(a) It measure potential in the open circuit.
(b) It uses sensitive galvanometer for null detection.
(c) It uses high resistance potentiometer wire.
(d) It measures potential in the closed circuit.
Answer:
(a) It measure potential in the open circuit.
Question 30.
Electromotive force is most closely related to
(a) electric field
(b) magnetic field
(c) potential difference
(d) mechanical force
Answer:
(c) potential difference
Question 31.
The capacitance of a pure capacitor is 1 farad. In DC circuit, the effective resistance will be
(a) zero
(b) infinite

(c) $1 \Omega$
(d) $0.5 \Omega$
Answer:
(b) infinite
Question 32 .
The resistance of an ideal ammeter is
(a) zero
(b) small
(c) high
(d) infinite
Answer:
(a) zero
Question 33.
A milliammeter of range $10 \mathrm{~mA}$ has a coil of resistance $1 \Omega$. To use it as a voltmeter of range $10 \mathrm{~V}$, the resistance that must be connected in series with it is
(a) $999 \Omega$
(b) $1000 \Omega$
(c) $9 \Omega$
(d) $99 \Omega$
Answer:
(a) $999 \Omega$
Hint:
$
\mathrm{R}=\frac{V}{I_g}-\mathrm{R}_{\mathrm{g}}=\frac{10}{10 \times 10^{-3}}-1=999 \Omega
$
Question 34 .
A battery of emf $10 \mathrm{~V}$ and internal resistance $3 \Omega$ is connected to a resistor. The current in the circuit is. $0.5 \mathrm{~A}$. The terminal voltage of the battery when the circuit is closed is
(a) $10 \mathrm{~V}$
(b) zero
(c) $8.5 \mathrm{~V}$
(d) $1.5 \mathrm{~V}$
Answer:
(c) $8.5 \mathrm{~V}$
Hint:
$
\mathrm{V}=\xi-\mathrm{Ir}=10-(0.5 \times 3)=8.5 \mathrm{~V}
$

Question 35.
Good resistance coils are made of
(a) copper
(b) manganin
(c) iron
(d) aluminium
Answer:
(b) manganin
Question 36.
A wire of resistance $\mathrm{R}$ is stretched to three times its original length. The new resistance is
(a) $3 R$
(b) $9 \mathrm{R}$
(c) $\mathrm{R} / 3$
(d) $\mathrm{R} / 9$
Answer:
(b) $9 \mathrm{R}$
Question 37.
n resistances, each of $\mathrm{r} \Omega$, when connected in parallel give an equivalent resistance of $\mathrm{R} \Omega$. If these resistances were connected in series, the combination would have a resistance in horns equal to
(a) $\mathrm{n}^2 \mathrm{R}$
(b) $\frac{R}{n^2}$
(c) $\frac{R}{n}$
(d) $\mathrm{nR}$
Answer:
(a) $\mathrm{n}^2 \mathrm{R}$
Hint:
Resistance in parallel combination, $\mathrm{R}=\frac{r}{n} \Rightarrow \mathrm{r}=\mathrm{Rn}$
Resistance in series combination, $\mathrm{R}^{\prime}=\mathrm{nr}=\mathrm{n}^2 \mathrm{R}$

Question 38.
When a wire of uniform cross-section, having resistance $\mathrm{R}$, is bent into a complete circle, the resistance between any two of diametrically opposite points will be
(a) $\frac{R}{8}$
(b) $\frac{R}{2}$
(c) $4 \mathrm{R}$
(d) $\frac{R}{4}$
Answer:
(d) $\frac{R}{4}$
Hint:
It becomes two resistors each of $(\mathrm{d}) \frac{R}{2}$, connected in parallel.
Question 39.
A steady current is set up in a metallic wire of non uniform cross-section. How is the rate of flow $\mathrm{K}$ of electrons related to the area of cross-section $A$ ?
(a) $\mathrm{K}$ is independent of $\mathrm{A}$
(b) $\mathrm{K} \propto \mathrm{A}$
(c) $\mathrm{K} \propto \mathrm{A}^{-1}$
(d) $K \propto A^2$
Answer:
(c) $\mathrm{K} \propto \mathrm{A}^{-1}$
Question 40.
Ohm's Law is not obeyed by
(a) electrolytes
(b) discharge tubes
(c) vacuum tubes
(d) all of these
Answer:
(d) all of these

Question 41.
Which of the following has negative temperature coefficient of resistance?
(a) Copper
(b) Aluminium
(c) Germanium
(d) Iron
Answer:
(c) Germanium
II. Fill in the blanks
Question 1.
The material through which electric charge can flow easily is .......
Answer:
Copper.
Question 2.
A toaster operating at $240 \mathrm{~V}$ has a resistance of $120 \Omega$. The power is ..................
Answer:
$480 \mathrm{~W}$
Question 3.
In the case of insulators, as the temperature decreases, resistivity ....................
Answer:
Increases.
Question 4.
When $\mathrm{n}$ resistors of equal resistance (R) are connected in series, the effective resistance is ............
Answer:
$\mathrm{nR}$.
Question 5.
The net flow of charge at any point in the conductor is ...............
Answer:
Zero.
Question 6.
The flow of free electrons in a conductor constitutes ...............
Answer:
Electric current.
Question 7.
The rate of flow of charge through any wire is called ..........
Answer:
Current.

Question 8.
The drift velocity acquired per unit electric field is the ...............
Answer:
Mobility.
Question 9.
The reciprocal of resistance is ................
Answer:
Conductance.
Question 10 .
The unit of specific resistance is ......................
Answer:
Ohm meter.
Question 11.
The reciprocal of electrical resistivity is called ...................
Answer:
Electrical conductivity.
Question 12 .
With increase in temperature the resistivity of metals ....................
Answer:
Increases.
Question 13.
The resistivity of insulators is of the order of ..............
Answer:
$10^8 10^{14} \Omega \mathrm{m}$
Question 14.
The resistivity of semiconductors is of the order of ...................
Answer:
$10^{-2}-10^2 \Omega \mathrm{m}$
Question 15.
The materials which conduct electricity at zero resistance are called .................
Answer:
Superconductors.

Question 16.
Conductors turn into superconductors at .......................
Answer:
Low temperatures.
Question 17.
The resistance of superconductors is ...................
Answer:
Zero.
Question 18.
The phenomenon of superconductivity was discovered by ...............
Answer:
Kammerlingh onnes.
Question 19.
Mercury becomes a superconductor at ........................
Answer:
$4.2 \mathrm{~K}$
Question 20.
With increase of temperature, resistance of conductors ............
Answer:
increases
Question 21.
In insulators and semiconductors, as temperature increases, resistance .................
Answer:
Decreases.
Question 22.
A material with a negative temperature coefficient is called a ..............
Answer:
Thermistor.
Question 23.
The temperature coefficient for alloys is ..............
Answer:
Low.

Question 24.
The electric current in an external circuit flows from the ................
Answer:
Positive to negative terminal.
Question 25.
In the electrolyte of the cell, current flows from ...............
Answer:
Negative to positive terminal.
Question 26.
A freshly prepared cell has internal resistance. ....................
Answer:
Low.
Question 27.
Kirchhoff's first law is ............
Answer:
Current law.
Question 28.
The current law states that the algebraic sum of the currents meeting at any junction in a circuit is .................
Answer:
Zero.

Question 29.
Current law is a consequence of conservation of ..............
Answer:
Charges.
Question 30.
Kirchhoff's second law is .................
Answer:
Voltage law.
Question 31.
Kirchhoff's second law is a consequence of conservation of .................
Answer:
Energy.
Question 32.
Wheatstone bridge is an application of ...............
Answer:
Kirchhoff's Law.
Question 33

................. is a form of Wheatstone's bridge.
Answer:
Metre bridge.
Question 34.
The temperature coefficient of manganin wire is .............
Answer:
Low.
Question 35

..................is an instrument to measure potential difference.
Answer:
Potentiometer.
Question 36.
Unit of electrical energy is ....................
Answer:
Joule.
Question 37.
An instrument to measure electrical power consumed is .........
Answer:
Watt meter.

Question 38.

.................. first introduced the electrochemical battery
Answer:
Volta.
Question 39.
Charging is a process of reproducing ..............
Answer:
Active materials.
III. Match the following
Question 1.

Answer:
(i) $\rightarrow$ (b)
(ii) $\rightarrow$ (a)
(iii) $\rightarrow(\mathrm{d})$
(iv) $\rightarrow$ (c)

Question 2.

Answer:
(i) $\rightarrow$ (b)
(ii) $\rightarrow$ (c)
(iii) $\rightarrow$ (d)
(iv) $\rightarrow$ (a)

Question 3.

Answer:
(i) $\rightarrow$ (d)
(ii) $\rightarrow$ (c)
(iii) $\rightarrow$ (b)
(iv) $\rightarrow$ (a)
Question 4.

Answer:
(i) $\rightarrow(\mathrm{b})$
(ii) $\rightarrow(\mathrm{d})$
$($ iii $) \rightarrow($ a)
$(\mathrm{iv}) \rightarrow(\mathrm{c})$
IV.Assertion and reason type
(a) If both assertion and reason are true and the reason in the correct explanation of the assertion.
(b) If both assertion and reason are true but the reason is not correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Question 1.
Assertion: Fuse wire must have high resistance and low melting point.
Reason: Fuse is used for small current flow only
Answer:
(c) If assertion is true but reason is false.
Question 2.
Assertion: In practical application, power rating of resistance is not important.
Reason: Property of resistance remains same even at high temperature
Answer:
(d) If the assertion and reason both are false.
Question 3.
Assertion: Electric appliances with metallic body e.g. heaters, presses, etc, have three pin connections, whereas an electric bulb has two pins.
Reason: Three pin connection reduce heating of connecting cables.
Answer:
(c) If assertion is true but reason is false.

Short Answer Questions
Question 1.
Define current?
Answer:
Current is defined as a net charge $\mathrm{Q}$ passes through any cross section of a conductor in time $t$ then, $\mathrm{I}=\frac{Q}{t}$.
Question 2.
Define instantaneous current?
Answer:
The instantaneous current $\mathrm{I}$ is defined as the limit of the average current, as $\Delta \mathrm{t} \rightarrow 0$.
$
\mathrm{I}=\lim _{\Delta t \rightarrow 0} \frac{\Delta \mathrm{Q}}{\Delta t}=\frac{d \mathrm{Q}}{d t}
$
Question 3.
What is resistance? Give its unit?
Answer:
The resistance is the ratio of potential difference across the given conductor to the current passing through the conductor $\mathrm{V}$.
$
\mathrm{R}=\frac{V}{I}
$
Question 4.
What is meant by transition temperature?
Answer:
The resistance of certain materials become zero below certain temperature $T_c$. This temperature is known as critical temperature or transition temperature.
Question 5.
What is Joule's heating effect?
Answer:
When current flows through a resistor, some of the electrical energy delivered to the resistor is converted into heat energy and it is dissipated. This heating effect of current is known as Joule's heating effect.

Question 6.
What is meant by thermoelectric effect?
Answer:
Conversion of temperature differences into electrical voltage and vice versa is known as thermoelectric effect.
Question 7.
What is a thermopile? On what principle does it work?
Answer:
Thermopile is a device used to detect thermal radiation. It works on the principle of seebeck effect.
Question 8 .
What is a thermistor?
Answer:
A material with a negative temperature coefficient is called a thermistor.
$\mathrm{Eg}$ :
1. Insulator
2. Semiconductor.
Question 9.
State principle of potentiometer?
Answer:
The principle of potentiometer states that the emf of the cell is directly proportional to its balancing length.
$\xi \propto 1$
$
\breve{\zeta}=\operatorname{Irl} .
$

Long Answer Questions
Question 1.
Explain the concept of colour code for carbon resistors.
Answer:
Color code for Carbon resistors:
Carbon resistors consists of a ceramic core, on which a thin layer of crystalline carbon is deposited. These resistors are inexpensive, stable and compact in size. Color rings are used to indicate the value of the resistance according to the rules.
Three coloured rings are used to indicate the values of a resistor: the first two rings are significant figures of resistances, the third ring indicates the decimal multiplier after them. The fourth color, silver or gold, shows the tolerance of the resistor at $10 \%$ or $5 \%$. If there is no fourth ring, the tolerance is $20 \%$. For the resistor, the first digit $=5$ (green), the second digit $=6$ (blue), decimal multiplier $=10^3$ (orange) and tolerance $=5 \%$ (gold). The value of resistance $=56 \times 10^3 \mathrm{Q}$ or $56 \mathrm{k} \Omega$ with the tolerance value $5 \%$.
Question 2.
Explain in details of temperature dependence of resistivity.
Answer:
Temperature dependence of resistivity:
The resistivity of a material is dependent on temperature. It is experimentally found that for a wide range of temperatures, the resistivity of a conductor increases with increase in temperature according to the expression,
$
\rho_{\mathrm{T}}=\rho_0\left[1+\alpha\left(\mathrm{T}-\mathrm{T}_0\right)\right] \ldots \ldots(1)
$
where $\rho_{\mathrm{T}}$ is the resistivity of a conductor at $\mathrm{T}_0 \mathrm{C}, \rho_0$ is the resistivity of the conductor at some reference temperature To (usually at $20^{\circ} \mathrm{C}$ ) and a is the temperature coefficient of resistivity. It is defined as the ratio of increase in resistivity per degree rise in temperature to its resistivity at $\mathrm{T}_0$.
From the equation (1), we can write
$
\begin{aligned}
& \rho_{\mathrm{T}}-\rho_0=\alpha \rho_0\left(\mathrm{~T}-\mathrm{T}_0\right) \\
& \therefore \alpha=\frac{\rho_{\mathrm{T}}-\rho_0}{\rho_0\left(\mathrm{~T}-\mathrm{T}_0\right)}=\frac{\Delta p}{\rho_0 \Delta T}
\end{aligned}
$
where $\Delta_\rho=\rho_{\mathrm{T}}-\rho_0$ is change in resistivity for a change in temperature $\Delta \mathrm{T}=\mathrm{T}-\mathrm{T}_0$. Its unit is per ${ }^{\circ} \mathrm{C}$.
1. $\alpha$ of conductors:
For conductors a is positive. If the temperature of a conductor increases, the average kinetic energy of electrons in the conductor increases. This results in more frequent collisions and hence the resistivity increases. Even though, the resistivity of conductors like metals varies linearly for wide range of temperatures, there also exists a nonlinear region at very low temperatures. The resistivity approaches some finite value as the temperature approaches absolute zero. As the resistance is directly proportional to resistivity of the material, we can also write the resistance of a conductor at temperature $\mathrm{T}^{\circ} \mathrm{C}$ as
$
\mathrm{R}_{\mathrm{T}}-\mathrm{R}_0=\left[1+\alpha\left(\mathrm{T}-\mathrm{T}_0\right)\right] \ldots \ldots(2)
$
The temperature coefficient can be also be obtained from the equation (2), +

$
\begin{aligned}
\mathrm{R}_{\mathrm{T}}-\mathrm{R}_0 & =\alpha \mathrm{R}_0\left(\mathrm{~T}-\mathrm{T}_0\right) \\
\therefore \quad \alpha & =\frac{\mathrm{R}_{\mathrm{T}}-\mathrm{R}_0}{\mathrm{R}_0\left(\mathrm{~T}-\mathrm{T}_0\right)}=\frac{\Delta \mathrm{R}}{\mathrm{R}_0 \Delta \mathrm{T}} \\
\alpha & =\frac{\Delta \mathrm{R}}{\mathrm{R}_0 \Delta \mathrm{T}}
\end{aligned}
$
where $\Delta \mathrm{R}=\mathrm{R}_{\mathrm{T}}-\mathrm{R}_0$ is change in resistance during the change in temperature $\Delta \mathrm{T}=\mathrm{T}-\mathrm{T}_0$
2. $\alpha$ of semiconductors:
For semiconductors, the resistivity decreases with increase in temperature. As the temperature increases, more electrons will be liberated from their atoms (Refer unit 9 for conduction in semi conductors). Hence the current increases and therefore the resistivity decreases. A semiconductor with a negative temperature coefficient of resistance is called a thermistor.
We can understand the temperature dependence of resistivity in the following way. The electrical conductivity, $\sigma=\frac{n e^2 \tau}{m} \frac{m}{n e^2 \tau}$. As the resistivity is inverse of $\sigma$, it can be written as, $\sigma=\frac{n e^2 \tau}{m} \frac{m}{n e^2 \tau}$
The resistivity of materials is
1. inversely proportional to the number density (n) of the electrons
2. inversely proportional to the average time between the collisions ( $\tau$ ).
In metals, if the temperature increases, the average time between the collision $(\tau)$ decreases and $\mathrm{n}$ is independent of temperature. In semiconductors when temperature increases, $\mathrm{n}$ increases and $\tau$ decreases, but increase in $\mathrm{n}$ is dominant than decreasing $\mathrm{x}$, so that overall resistivity decreases.
Question 3.
Explain the effective internal resistance of cells connected in series combination. Compare the results to the external resistance.
Answer:
Cells in series Several cells can be connected to form a battery. In series connection, the negative terminal of one cell is connected to the positive terminal of the second cell, the negative terminal of second cell is connected to the positive terminal of the third cell and so on. The free positive terminal of the first cell and the free negative terminal of the last cell become the terminals of the battery.

Suppose $\mathrm{n}$ cells, each of emf $\zeta$ volts and internal resistance $\mathrm{r}$ ohms are connected in series with an external resistance $\mathrm{R}$.
The total emf of the battery $=\mathrm{n} \xi$
The total resistance in the circuit $=\mathrm{nr}+\mathrm{R}$
By Ohm's law, the current in the circuit is
$
\mathrm{I}=\frac{\text { total emf }}{\text { total resistance }}=\frac{n \xi}{n r+\mathrm{R}}
$
Case (a) If $r $
\mathrm{I}=\frac{n \xi}{R} \mathrm{nI}_1 \approx \mathrm{nI}_1
$
where, $\mathrm{I}$, is the current due to a single cell $\left(\mathrm{I}_1=\frac{\xi}{\mathrm{R}}\right)$
Thus, if $\mathrm{r}$ is negligible when compared to $\mathrm{R}$ the current supplied by the battery is $\mathrm{n}$ times that supplied by a single cell.
Case (b) If $\mathrm{r} \gg>\mathrm{R}, \mathrm{I}=\frac{n \xi}{n r} \approx \frac{\xi}{R} \ldots \ldots$. (3)
It is the current due to a single cell. That is, current due to the whole battery is the same as that due to a single cell and hence there is no advantage in connecting several cells. Thus series connection of cells is advantageous only when the effective internal resistance of the cells is negligibly small compared with $\mathrm{R}$.
Question 4.
Explain the effective internal resistance of cells connected in parallel combination. Compare the results to the external resistance.
Answer:
Cells in parallel: In parallel connection all the positive terminals of the cells are connected to one point and all the negative terminals to a second point. These two points form the positive and negative terminals of the battery.
Let $\mathrm{n}$ cells be connected in parallel between the points $\mathrm{A}$ and $\mathrm{B}$ and a resistance $\mathrm{R}$ is connected between the points $\mathrm{A}$ and $\mathrm{B}$. Let $\xi$, be the emf and $\mathrm{r}$ the internal resistance of each cell.
The equivalent internal resistance of the battery is $\frac{1}{r_{\text {eq }}}=\frac{1}{r}+\frac{1}{r}+\ldots . \frac{1}{r}$ (n terms) $=\frac{n}{r}$.
So $\mathrm{r}_{\mathrm{eg}}=\frac{r}{n}$ and the total resistance in the circuit $=\mathrm{R}+\frac{r}{n}$. The total emf is the potential difference between the points $\mathrm{A}$ and $\mathrm{B}$, which is equal to $\xi$. The current in the circuit is given by

$
\begin{aligned}
& \mathrm{I}=\frac{\xi}{\frac{r}{n}+\mathrm{R}} \\
& \mathrm{I}=\frac{n \xi}{r+n \mathrm{R}}
\end{aligned}
$
Case (a) If $r where II is the current due to a single cell and is equal to $\frac{\xi}{R}$ when $\mathrm{R}$ is negligible. Thus, the current through the external resistance due to the whole battery is $\mathrm{n}$ times the current due to a single cell.
Case (b) If $\mathrm{r}<<\mathrm{R} . \mathrm{I}=\frac{\xi}{R} \ldots$. (3)
The above equation implies that current due to the whole battery is the same as that due to a single cell. Hence it is advantageous to connect cells in parallel when the external resistance is very small compared to the internal resistance of the cells.