Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R=10.0 Ω is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. The value of X is:

1. $12.1\Omega$

2. $12.4 \Omega$

3. $10.3 \Omega$

4. $11.7 \Omega$

The figure shows a 2.0 V potentiometer used for the determination of the internal resistance of a 1.5 V cell. The balance point of the cell in the open circuit is 76.3 cm. When a resistor of 9.5 Ω is used in the external circuit of the cell, the balance point shifts to 64.8 cm length of the potentiometer wire. The internal resistance of the cell is:
    
1. \(1.68~\Omega \)
2. \(0.13~\Omega \)
3. \(0.31~\Omega \)
4. \(1.12~\Omega \)

A potential difference of 10 V is applied across a conductor of $1000 \mathrm{\Omega }$. The number of electrons flowing through the conductor in 300 sec is:

1. $1.875\times {10}^{16}$

2. $1.875\times {10}^{17}$

3. $1.875\times {10}^{22}$

4. $1.875\times {10}^{19}$

Ohm's law fails in:

1. Diode

2. Thyristor

3. PN junction system

4. All of these

Identical pieces of Ge and Cu are taken and cooled, then:

1. Resistivity of both increases

2. Resistivity of both decreases

3. Resistivity of Cu increases and Ge decreases

4. Resistivity of Cu decreases and Ge increases

A potential difference of 5 V is applied across a conductor of length 10 cm. If the drift velocity of electrons is $2.5\times {10}^{-4}$ m/s, then the electron mobility will be:

1. $5\times {10}^{-4} {\mathrm{m}}^2 {\mathrm{V}}^{-1} {\mathrm{s}}^{-1}$

2. $5\times {10}^{-6} {\mathrm{m}}^2 {\mathrm{V}}^{-1} {\mathrm{s}}^{-1}$

3. $5\times {10}^{-2 }{\mathrm{m}}^2 {\mathrm{V}}^{-1} {\mathrm{s}}^{-1}$

4. Zero

The resistance of a rectangular block of copper of dimensions $2 \mathrm{mm}\times 2 \mathrm{mm}\times 5 \mathrm{m}$ between two square faces is $0.02\mathrm{\Omega }$. What is the resistivity of copper?

1. $1.6\times {10}^{-8} \mathrm{\Omega }$

2. $1.6\times {10}^{-6} \mathrm{\Omega }-\mathrm{m}$

3. $1.6\times {10}^{-8} \mathrm{\Omega }-\mathrm{m}$

4. Zero

Two wires A and B of the same material, having radii in the ratio of 1: 2 carry currents in the ratio of 4: 1. The ratio of the drift speed of electrons in A and B is:

1. 16: 1

2. 1: 16

3. 1: 4

4. 4: 1

If a copper wire is stretched to make its radius decrease by 0.1%, then the percentage increase in resistance is nearly:

1. 0.1%

2. 0.8%

3. 0.4%

4. 0.2%

A certain piece of copper is to be shaped into a conductor of minimum resistance. Its length and diameter should respectively be:

1. L, D

2. 2L, $\frac{\mathrm{D}}{2}$

3. $\frac{\mathrm{L}}{2}$, 2D

4. $\mathrm{L}, \frac{\mathrm{D}}{2}$