CBSE Class 12 · 2008 · Current ElectricityShort Answer

Two wires X and Y have the same resistivity, but their cross-sectional areas are in the ratio

2 : 3

and their lengths in the ratio

1 : 2

. They are first connected in series and then in parallel to a DC source. Find the ratio of the drift speeds of the electrons in the two wires in the two cases.

Solution

Series — the same current

I

flows through both, and

v_{d} = \frac{I}{n e A} \propto \frac{1}{A}

, so

\frac{( v _{d} ) _{X}}{( v _{d} ) _{Y}} = \frac{A _{Y}}{A _{X}} = \frac{3}{2}

. Parallel — the same voltage acts across each, and

v_{d} = \frac{e τ}{m} \frac{V}{ℓ} \propto \frac{1}{ℓ}

, so

\frac{( v _{d} ) _{X}}{( v _{d} ) _{Y}} = \frac{ℓ _{Y}}{ℓ _{X}} = \frac{2}{1}

CBSE Class 12 Board · 2008 · Subjective

Practise more: all CBSE board PYQs on Current Electricity →

More board questions on Current Electricity

An ammeter and a voltmeter are connected in series to a battery, their readings being $A$ and $V$ respectively. If a resistor is now connected in parallel with the voltmeter, then:
CBSE 2024View solution →
A galvanometer shows full-scale deflection for a current $I_{g}$ . With a shunt $S_{1}$ it becomes an ammeter of range $(0 - I)$ ; with a shunt $S_{2}$ its range becomes $(0 - 2 I)$ . Then $\frac{S _{1}}{S _{2}}$ is:
CBSE 2024View solution →
(i) Define the 'temperature coefficient of resistance' of a metal.
(ii) Show the variation of the resistivity of copper with a rise in temperature.
(iii) The resistance of a wire is $10 Ω$ at $2 7^{\circ} C$ . Find its resistance at $- 3^{\circ} C$ , given the temperatu …
CBSE 2024View solution →
A current of $0.8 A$ flows in a conductor of $40 Ω$ for 1 minute. The heat produced in the conductor will be:
CBSE 2023View solution →
A cell of EMF $E$ is connected across an external resistance $R$ . When a current $I$ is drawn from the cell, the potential difference across its electrodes drops to $V$ . The internal resistance $r$ of the cell is:
CBSE 2023View solution →
Define current density and relaxation time. Derive an expression for the resistivity of a conductor in terms of the number density of charge carriers and the relaxation time.
CBSE 2023View solution →