Conductivity and Resistivity

Q. The specific resistance of manganin is $50\times {10}^{-8}\Omega m$. The resistance of a manganin cube having length 50 cm is

1. ${10}^{-6}\Omega$
2. $2.5\times {10}^{-5}\Omega$
3. ${10}^{-8}\Omega$
4. $5\times {10}^{-4}\Omega$

Q. In a balanced wheatstone bridge, current in the galvanometer is zero. It remains zero when
$\left(1\right)$ The emf is increased
$\left(2\right)$ All resistance are increased by $10\Omega$
$\left(3\right)$ All resistance are made five times.
$\left(4\right)$ The battery and the galvanometer are interchanged.

1. Only $\left(1\right)$ is correct.
2. $\left(1\right)$ and $\left(3\right)$ are correct.
3. $\left(1\right),\left(2\right)$ and $\left(3\right)$ are correct.
4. $\left(1\right),\left(3\right)$ and $\left(4\right)$ are correct.

Q. A rod of certain metal is 1 m long and 0.6 cm in diameter. It’s resistance is $3\times {10}^{-3}\Omega$. A disc of the same metal is 1 mm thick and 2 cm in diameter, what is the resistance between it’s circular faces.

1. $1.35\times {10}^{-6}\Omega$
2. $2.7\times {10}^{-7}\Omega$
3. $4.05\times {10}^{-6}\Omega$
4. $8.1\times {10}^{-6}\Omega$

Q. Two metal wires of identical dimensions are connected in series. If ${\sigma }_1$ and ${\sigma }_2$ are the conductivities of the metals respectively, the effective conductivity of the combination is

1. ${\sigma }_1+{\sigma }_2$
2. $\frac{{\sigma }_1+{\sigma }_2}{2}$
3. $\sqrt{{\sigma }_1{\sigma }_2}$
4. $\frac{{\sigma }_1{\sigma }_2}{{\sigma }_1+{\sigma }_2}$

Q. A conducting medium is shaped in a form of a quarter annulus of radius b and a (b > a) and thickness t. Resistivity of material is $\rho$.
[CD = AB = EF = GH = t]

1. Resistance between faces ABCD and EFGH is $\frac{\pi \rho }{2tln\left(\frac{b}{a}\right)}$
2. Resistance between faces BCGF and ADHE is $\frac{4\rho t}{\pi (b^2-a^2)}$
3. Resistance between faces ABFE and CDHG is $\frac{2\rho }{\pi t}ln\left(\frac{b}{a}\right)$
4. Resistance between faces ABCD and EFGH is $\frac{\rho \pi (a+b)}{\mu (b-a)t}$

Q.

Find the resistance of a hollow cylinder of inner radius a and outer radius b whose inner and outer cylindrical surfaces are connected by to a p.d ($\rho$ resistivity)

1. $\frac{\rho l}{\pi ab}$
2. $\frac{\rho }{2\pi r}ln\left(\frac{b}{a}\right)$
3. $\frac{\rho }{\pi r}ln\left(\frac{b}{a}\right)$
4. $\frac{2\rho }{\pi r}ln\left(\frac{b}{a}\right)$

Q. If the resistance of a conductor is $5\Omega$ at ${50}^{\circ }C$ and $7\Omega$ at ${100}^{\circ }C$, then the mean temperature coefficient of resistance is

1. $0.01{\left({}^{\circ }C\right)}^{-1}$
2. $0.04{\left({}^{\circ }C\right)}^{-1}$
3. $0.06{\left({}^{\circ }C\right)}^{-1}$
4. $0.08{\left({}^{\circ }C\right)}^{-1}$

Q. A moving-coil galvanometer has $100\text{turns}$ and each turn has an area $2.0{\text{cm}}^2$. The magnetic field produced by the magnet is $0.01\text{T}$. The deflection in the coil is $0.05\text{radian}$ when a current of $10\text{mA}$ is passed through it. Find the torsional constant of the suspension wire.

1. $1.0\times {10}^{-5}\text{Nm/rad}$
2. $2.0\times {10}^{-5}\text{Nm/rad}$
3. $4.0\times {10}^{-5}\text{Nm/rad}$
4. $3.0\times {10}^{-5}\text{Nm/rad}$

Q. Iron-man needs a better suit to resist Thor’s lightning. What should he change to do this, given that he can’t change the dimensions (size and shape) of the suit.

1. Change the name of the suit.
2. Change the material of the suit.
3. Change the colour of the suit.
4. Change the batteries of the suit.

Q. What is the unit of conductivity and resistivity respectively?

1. Ohm, mho
2. Mho, ohm
3. Ohm m, mho/m
4. Mho/m, ohm m

Q. The conductivity of a material is 5 mho/m. What is it’s resistivity?

1. 5 ohm m
2. 0.2 ohm m
3. 25 ohm m
4. None of these.

Q. Find the resistance of a hollow sphere whose inner surface (radius :a) and outer surface (radius b) are connected to a p.d E($\rho$:resistivity)

1. $\frac{\rho (b-a)}{4\pi ab}$
2. $\frac{\rho ab}{4\pi (b-a)}$
3. $\frac{\rho (b+a)}{4\pi ab}$
4. $\frac{\rho ab}{4\pi (b+a)}$

Q. An aluminium rod of length 3.14 m is of square cross-section $3.14\times 3.14m{m}^2$. What should be the radius of 1 m long another rod of same material to have equal resistance

1. 2 mm
2. 4 mm
3. 1 mm
4. 6 mm

Q. Find the resistance of the truncated cone as shown.

1. $\frac{\rho l}{\pi ab}$
2. $\frac{\rho }{\pi r}ln\left(\frac{b}{a}\right)$
3. $\frac{\rho (b-a)}{ab}$
4. $\frac{\rho ab}{\pi r}$

Q. A material has a resistivity of 5 ohm m. The potential difference across the material was increased by a factor of 10. What is the new resistivity?

1. 5 ohm m
2. 50 ohm m
3. 500 ohm m
4. 0.5 ohm m

Q. For whatever reason, the relaxation time of a conductor increases by a factor of 2 and the number of electrons per unit volume decreases by a factor of 3. Given all other factors remain the same, the new conductivity changes by what factor?

1. $\frac{2}{3}$
2. $\frac{3}{2}$
3. $6$
4. $\frac{1}{6}$

Q. A moving-coil galvanometer has $100\text{turns}$ and each turn has an area $2.0{\text{cm}}^2$. The magnetic field produced by the magnet is $0.01\text{T}$. The deflection in the coil is $0.05\text{radian}$ when a current of $10\text{mA}$ is passed through it. Find the torsional constant of the suspension wire.

1. $1.0\times {10}^{-5}\text{Nm/rad}$
2. $4.0\times {10}^{-5}\text{Nm/rad}$
3. $3.0\times {10}^{-5}\text{Nm/rad}$
4. $2.0\times {10}^{-5}\text{Nm/rad}$

Q. Length of a hollow tube is 5m, it’s outer diameter is 10 cm and thickness of it’s wall is 5 mm. If resistivity of the material of the tube is $1.7\times {10}^{-8}\Omega m$ then the resistance of the tube will be

1. $5.6\times {10}^{-5}\Omega$
2. $2\times {10}^{-5}\Omega$
3. $4\times {10}^{-5}\Omega$
4. None of these

Q. Minimum number of $8\mu \text{F}$ and $250\text{V}$ capacitors used to make a combination of $16\mu \text{F}$ and $1000\text{V}$ are:

1. $4$
2. $8$
3. $16$
4. $32$

Q. The resistivity of potentiometer wire is ${10}^{-7}\Omega m$ and its area of cross-section is ${10}^{-6}{m}^2$. When a current $i=0.1A$ flows through the wire, its potential gradient is

1. ${10}^{-2}V/m$
2. ${10}^{-4}V/m$
3. $0.1V/m$
4. $10V/m$

Q. The conductivity of a material is 5 mho/m. What is it’s resistivity?

1. 5 ohm m
2. 0.2 ohm m
3. 25 ohm m
4. None of these.