A metal wire of cross-sectional area 0.5 mm² and length 100 m is connected across a battery of e.m.f. 2 V and internal resistance 1 Ω. The density, atomic mass and electrical conductivity of the metal are 6.35 × 10³ kg m⁻³, 63.5 gm/mole and 2 × 10⁸ mho m⁻¹, respectively. Assuming one conduction electron per atom of the metal, the drift velocity (in mm s⁻¹) of the electrons in the wire is:

[Take Avogadro’s number as 6 × 10²³ and charge of the electron as 1.6 × 10⁻¹⁹ C.]

During an experiment with a metre bridge, the galvanometer shall a null point when the jockey is pressed at 40.0 cm using a standard resistance of 90$$\Omega$$, as shown in the figure. The least count of the scale used in the meter bridge is 1 mm. The unknown resistance is

A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers' end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with power factor unity. All the currents and voltages mentioned are rms values.

If the direct transmission method with a cable of resistance 0.4 $$\Omega$$ km^$$-$$1 is used, the power dissipation (in %) during transmission is