Ohm's Law, Resistivity & Temperature

In case of thermistor, which one of the following statements is 'WRONG'?

Which of the following graph represents the temperature (T) dependence of resistivity ($\rho$) of a semiconductor?

Consider two circuits, (A) and (B), each having two resistors. One of them has a positive temperature coefficient of resistance, $+\alpha$, while the other one has a negative temperature coefficient, $-\alpha$, as shown in the figure. The currents through these circuits are denoted by $I_A$ and $I_B$. At initial temperature, the resistance of the two resistors is $R_0$. As the temperature is increased, the correct option that describes the variation of current in these circuits is:

A resistor of $6\ \Omega$ with a tolerance of $10\%$ and another of $4\ \Omega$ with a tolerance of $10\%$ are connected in series. The tolerance of combination is about

Which of the following resistivity ( $\rho$) $\text{v/s}$ temperature ( T) curves is most suitable to be used in wire bound standard resistors?

At room temperature $(27^\circ\text{C})$, the resistance of a heating element is $50\ \Omega$. The temperature coefficient of the material is $2.4 \times 10^{-4}\ {}^\circ\text{C}^{-1}$. The temperature of the element, when its resistance is $62\ \Omega$, is __________ ${}^\circ\text{C}$.

To determine the resistance (R) of a wire, a circuit is designed below. The $V\text{-}I$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $R$ is _________ $\Omega$.

Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0\text{ mm}$ and wire $B$ has radius of $4.0\text{ mm}$. The resistance of wire $B$ is $2\ \Omega$. The resistance of wire $A$ is ________ $\Omega$.

A wire of resistance $R$ and radius $r$ is stretched till its radius became $r/2$. If new resistance of the stretched wire is $xR$, then value of $x$ is ________.

Two conductors have the same resistances at $0^\circ\text{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients for their series and parallel combinations are:

An electric toaster has resistance of $60\ \Omega$ at room temperature $(27^\circ\text{C})$. The toaster is connected to a $220\text{ V}$ supply. If the current flowing through it reaches $2.75\text{ A}$, the temperature attained by toaster is around: ( if $\alpha = 2 \times 10^{-4}/^\circ\text{C}$)

Resistance of a wire at $0^\circ\text{C}, 100^\circ\text{C}$ and $t^\circ\text{C}$ is found to be $10\ \Omega, 10.2\ \Omega$ and $10.95\ \Omega$ respectively. The temperature $t$ in Kelvin scale is _________.

A certain wire $\text{A}$ has resistance $81\ \Omega$. The resistance of another wire $\text{B}$ of same material and equal length but of diameter thrice the diameter of A will be:

A rectangular parallelopiped is measured as $1\text{ cm} \times 1\text{ cm} \times 100\text{ cm}$. If its specific resistance is $3 \times 10^{-7}\ \Omega\text{ m}$, then the resistance between its two opposite rectangular faces will be ___________ $\times 10^{-7}\ \Omega$.

The resistance of a wire is 5 $\Omega$. Its new resistance in ohm if stretched to 5 times of its original length will be:

The resistance of platinum wire at $0^\circ\text{C}$ is $2\ \Omega$ and $6.8\ \Omega$ at $80^\circ\text{C}$. The temperature coefficient of resistance of the wire is:

Resistance of a carbon resistor determined from colour codes is $(22000 \pm 5\%)\ \Omega$. The colour of third band must be:

A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 $\times$ 10$-3$ kg, density is 8.92 $\times$ 10$3$ kg/m$3$ and resistivity is 1.7 $\times$ 10$^{-8}\ \Omega \cdot \text{m}$. The length of wire is:

The current flowing through a conductor connected across a source is $2\text{ A}$ and 1.2 $\text{A}$ at $0^\circ\text{C}$ and $100^\circ\text{C}$ respectively. The current flowing through the conductor at $50^\circ\text{C}$ will be ___________ $\times 10^{2}\text{ mA}$.

A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is $n \times 10^{-3}\ \Omega$. If the resistivity of the material is $2.4 \times 10^{-8}\ \Omega\text{ m}$, the value of $n$ is ___________.

A wire of resistance $160\ \Omega$ is melted and drawn in a wire of one-fourth of its length. The new resistance of the wire will be

The length of a metallic wire is increased by $20\%$ and its area of cross section is reduced by $4\%$. The percentage change in resistance of the metallic wire is __________.

If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is __________%.

The reciprocal of resistance is:

A wire of resistance R1 is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is:

An aluminium wire is stretched to make its length, 0.4% larger. The percentage change in resistance is:

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ____________ %.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils. Reason R: Constantan and manganin have very small value of temperature coefficient of resistance. In the light of the above statements, choose the correct answer from the options given below.

Resistance of the wire is measured as 2 $\Omega$ and 3 $\Omega$ at 10$^\circ$C and 30$^\circ$C respectively. Temperature co- efficient of resistance of the material of the wire is:

The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is 31.4 cm. The diameter of wire is measured as 2.4 cm. The resistivity of the given wire is measured as x $\times$ 10$-$3 $\Omega$ cm. The value of x is ____________. [Take $\pi$ = 3.14]

A $1\text{ m}$ long wire is broken into two unequal parts $\text{X}$ and $\text{Y}$. The $\text{X}$ part of the wire is streched into another wire W. Length of $W$ is twice the length of $X$ and the resistance of $\text{W}$ is twice that of $\text{Y}$. Find the ratio of length of $\text{X}$ and $\text{Y}$.

The resistance of a conductor at 15$^\circ$C is 16$\Omega$ and at 100$^\circ$ C is 20$\Omega$. What will be the temperature coefficient of resistance of the conductor?

The Colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is:

For the circuit shown, the value of current at time t = 3.2 s will be _________ A.

[Voltage distribution V(t) is shown by Fig. (1) and the circuit is shown in Fig. (2)]

A wire of 1$\Omega$ has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is:

What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3$\Omega$?

(Given resistivities of iron and copper-nickel alloy wire are 12 $\mu\Omega$ cm and 51 $\mu\Omega$ cm respectively)

Two solid conductors are made up of same material, have same length and same resistance. One of them has a circular cross section of area $A_1$ and the other one has a square cross section of area $A_2$. The ratio $A_1/A_2$ is

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity $\rho$C, $\rho$T, $\rho$M and $\rho$A respectively. Then:

Which of the following graph represents the variation of resistivity ($\rho$) with temperature (T) for copper?

The solids which have the negative temperature coefficient of resistance are:

The color code of a resistance is given below:

The values of resistance and tolerance, respectively, are

Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius ‘a’ and a concentric thin cylindrical shell of radius ‘b’ filled in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for:

For a metallic wire, the ratio of voltage to corresponding current is

A 200 $\Omega$ resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be:

A carbon resistance has a following colour code. What is the value of the resistance?

A resistance is shown in the figure. Its value and tolerance are given respectively by:

A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is:

In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that:

A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is -

Space between two concentric conducting spheres of radii a and b (b > a) is filled with a medium of resistivity $\rho$. The resistance between the two spheres will be:

A carbon resistor of (47 $\pm$ 4.7) k$\Omega$ is to be marked with rings of different colours for its identification. The colour code sequence will be

A heating element has a resistance of 100 $\Omega$ at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500oC more than room temperature. What is the temperature coefficient of resistance of the heating element?

The resistance of a wire is 'R' ohm. If it is melted and stretched to 'n' times its original length. its new resistance will be

A uniform wire of length l and radius r has a resistance of 100 $\Omega$. It is recast into a wire of radius $\frac{r}{2}.$ The resistance of new wire will be:

The resistance of an electrical toaster has a temperature dependence given by R(T) = R0 [1 + $\alpha$(T − T0)] in its range of operation. At T0 = 300 K, R = 100 $\Omega$ and at T = 500 K, R = 120 $\Omega$. The toaster is connected to a voltage source at 200 V and its temperature is raised at a constant rate from 300 to 500 K in 30 s. The total work done in raising the temperature is:

Suppose the drift velocity $v$d in a material varied with the applied electric field E as $v$d $\propto \sqrt{E}$. Then V - I graph for a wire made of such a material is best given by:

A wire of resistance 4 $\Omega$ is stretched to twice its original length. The resistance of stretched wire would be

Two rods are joined end to end, as shown. Both have a cross-sectional area of 0.01 cm2. Each is 1 $-$6

meter long. One rod is of copper with a resistivity of 1.7 $\times$ 10 ohm-centimeter, the other is of iron $-$5

with a resistivity of 10 ohm-centimeter.

How much voltage is required to produce a current of 1 ampere in the rods?

If a wire is stretched to make it $0.1\%$ longer, its resistance will:

Two conductors have the same resistance at $0^\circ\text{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2.$ The respective temperature coefficients of their series and parallel combinations are nearly

Statement - 1: The temperature dependence of resistance is usually given as $R = R_0(1 + \alpha\Delta t).$ The resistance of wire changes from $100\ \Omega$ to $150\ \Omega$ when its temperature is increased from $27^\circ\text{C}$ to $227^\circ\text{C}$. This implies that $\alpha = 2.5 \times 10^{-3}/\text{C}.$

Statement - 2: $R = R_0(1 + \alpha\Delta t)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R = (R - R_0) \ll R_0.$

A wire of a certain material is stretched slowly by ten percent. Its new resistance and specific resistance become respectively

Consider a block of conducting material of resistivity $\text{'}\rho\text{'}$ shown in the figure. Current $\text{'}I\text{'}$ enters at $\text{'}A\text{'}$ and leaves from $\text{'}D\text{'}$. We apply superposition principle to find voltage $\text{'}\Delta V\text{'}$ developed between $\text{'}B\text{'}$ and $\text{'}C\text{'}$. The calculation is done in the following steps:

(i) Take current $\text{'}I\text{'}$ entering from $\text{'}A\text{'}$ and assume it to spread over a hemispherical surface in the block.

(ii) Calculate field $E(r)$ at distance $\text{'}r\text{'}$ from A by using Ohm's law $E = \rho j,$ where $j$ is the current per unit area at $\text{'}r\text{'}$.

(iii) From the $\text{'}r\text{'}$ dependence of $E(r)$, obtain the potential $V(r)$ at $r$.

(iv) Repeat (i), (ii) and (iii) for current $\text{'}I\text{'}$ leaving $\text{'}D\text{'}$ and superpose results for $\text{'}A\text{'}$ and $\text{'}D\text{'}.$

$\Delta V$ measured between $B$ and $C$ is

Consider a block of conducting material of resistivity $\text{'}\rho\text{'}$ shown in the figure. Current $\text{'}I\text{'}$ enters at $\text{'}A\text{'}$ and leaves from $\text{'}D\text{'}$. We apply superposition principle to find voltage $\text{'}\Delta V\text{'}$ developed between $\text{'}B\text{'}$ and $\text{'}C\text{'}$. The calculation is done in the following steps:

(i) Take current $\text{'}I\text{'}$ entering from $\text{'}A\text{'}$ and assume it to spread over a hemispherical surface in the block.

(ii) Calculate field $E(r)$ at distance $\text{'}r\text{'}$ from A by using Ohm's law $E = \rho j,$ where $j$ is the current per unit area at $\text{'}r\text{'}$.

(iii) From the $\text{'}r\text{'}$ dependence of $E(r)$, obtain the potential $V(r)$ at $r$.

(iv) Repeat (i), (ii) and (iii) for current $\text{'}I\text{'}$ leaving $\text{'}D\text{'}$ and superpose results for $\text{'}A\text{'}$ and $\text{'}D\text{'}.$

For current entering at $A,$ the electric field at a distance $\text{'}r\text{'}$ from $A$ is

The resistance of a wire is $5$ ohm at $50^\circ\text{C}$ and $6$ ohm at $100^\circ\text{C}.$ The resistance of the wire at $0^\circ\text{C}$ will be

A material 'B' has twice the specific resistance of 'A'. A circular wire made of 'B' has twice the diameter of a wire made of 'A'. Then for the two wires to have the same resistance, the ratio $\ell_B/\ell_A$ of their respective lengths must be

The resistance of bulb filament is $100\ \Omega$ at a temperature of $100^\circ\text{C}.$ If its temperature coefficient of resistance be $0.005$ per $^\circ\text{C}$, its resistance will become $200\ \Omega$ at a temperature of

A material $'B'$ has twice the specific resistance of $'A'.$ A circular wire made of $'B'$ has twice the diameter of a wire made of $'A'$. Then for the two wires to have the same resistance, the ratio $l_B/l_A$ of their respective lengths must be

The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then

Thermistors are usually made of

The length of a given cylindrical wire is increased by $100\%$. Due to the consequent decrease in diameter the change in the resistance of the wire will be

Specific resistance of a conductor increases with

Copper and silicon is cooled from 300 K to 60 K, the specific resistance

The resistance of a discharge tube is

From the graph between current $(I)$ and voltage $(V)$ is shown below. Identify the portion corresponding to negative resistance

Three copper wires of lengths and cross-sectional areas are $(l, A),\ (2l, A/2)$ and $(l/2, 2A)$. Resistance is minimum in

In good conductors of electricity, the type of bonding that exists is

A wire $50\text{ cm}$ long and $1\text{ mm}^{2}$ in cross-section carries a current of $4\text{ A}$ when connected to a $2\text{ V}$ battery. The resistivity of the wire is

Identify the set in which all the three materials are good conductors of electricity

The masses of the wires of copper is in the ratio of $1 : 3 : 5$ and their lengths are in the ratio of $5 : 3 : 1$. The ratio of their electrical resistance is