The resistivity of iron is 1 × 10^–7 ohm – m. The resistance of iron wire of particular length and thickness is 1 ohm. If the length and the diameter of wire both are doubled, then the resistivity in ohm – m will be :

1. 1 × 10^–7

2. 2 × 10^–7

3. 4 × 10^–7

4. 8 × 10^–7

The resistivity of a wire :

Drift velocity \(v_d\) varies with the intensity of the electric field as per the relation:
1. \(v_{d} \propto E\)
2. \(v_{d} \propto \frac{1}{E}\)
3. \(v_{d}= \text{constant}\)
4. \(v_{d} \propto E^2\)

In a conductor 4 coulombs of charge flows for 2 seconds. The value of electric current will be :

1. 4 volts

2. 4 amperes

3. 2 amperes

4. 2 volts

The specific resistance of a wire is ρ, its volume is 3 m³ and its resistance is 3 ohms, then its length will be 

1. $\sqrt{\frac{1}{\rho }}$

2. $\frac{3}{\sqrt{\rho }}$

3. $\frac{1}{\rho }\sqrt{3}$

4. $\rho \sqrt{\frac{1}{3}}$ 

When a piece of aluminum wire of finite length is drawn through a series of dies to reduce its diameter to half its original value, its resistance will become :

1. Two times

2. Four times

3. Eight times

4. Sixteen times

The resistance of a wire of uniform diameter d and length L is R. The resistance of another wire of the same material but diameter 2d and length 4L will be :

1. 2R

2. R

3. R/2

4. R/4

There is a current of 1.344 amp in a copper wire whose area of cross-section normal to the length of the wire is 1 mm². If the number of free electrons per cm³ is 8.4 × 10²², then the drift velocity would be :

1. 1.0 mm/sec

2. 1.0 m/sec

3. 0.1 mm/sec

4. 0.01 mm/sec

An electric wire of length ‘I’ and area of cross-section a has a resistance R ohms. Another wire of the same material having the same length and area of cross-section 4a has a resistance of :

1. 4R

2. R/4

3. R/16

4. 16R

If \(n\), \(e\), \(\tau\) and \(m\) respectively represent the density, charge relaxation time and mass of the electron, then the resistance of a wire of length \(l\) and area of cross-section \(A\) will be:
1. \(\frac{ml}{ne^2\tau A}\)
2. \(\frac{m\tau^2A}{ne^2l}\)
3. \(\frac{ne^2\tau A}{2ml}\)
4. \(\frac{ne^2 A}{2m\tau l}\)