Advertisements
Advertisements
Question
Two conductors, made of the same material have equal lengths but different cross-sectional areas A1 and A2 (A1 > A2). They are connected in parallel across a cell. Show that the drift velocities of electrons in two conductors are equal.
Advertisements
Solution
When two wires are connected in parallel the potential difference across the wires will be the same.
V1 = V2 ...............(i)
V1 = Potential across wire A.
V2 = Potential across wire B.
Since two conductors are made up of the same material and have equal lengths, their resistivity will be the same,
`rho_1 = rho_2 = rho`
and `(R_2)/(R_1) = A_1/A_2` ........(ii)
Current (I1) flowing through the conductor with cross-sectional area A1 is given by
`I_1 = A_1n ev_1`
and `I_2 = A_2n ev_2` ..............(iii)
Since two conductors are connected in parallel.
I = I1 + I2
Using Ohm's law,
V = IR
From (i) I1R1 = I2R2
From (iii)
`A_1n ev_1R_1 = A_2n ev_2R_2`
`(A_1v_1)/(A_2v_2) = R_2/R_1`
From (ii)
`A_1/A_2 v_1/v_2 = A_1/A_2`
`v_1 = v_2`
Hence, the drift velocities of electrons in the two conductors are equal.
APPEARS IN
RELATED QUESTIONS
Derive an expression for drift velocity of free electrons.
Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 2·5 × 10−7 m2 carrying a current of 2·7 A. Assume the density of conduction electrons to be 9 × 1028 m−3
When electrons drift in a metal from lower to higher potential, does it mean that all the free electrons of the metal are moving in the same direction?
Consider the following statements.
(A) Free-electron density is different in different metals.
(B) Free-electron density in a metal depends on temperature.
Peltier Effect is caused _______________ .
Consider the following statements.
(A) Free-electron density is different in different metals.
(B) Free-electron density in a metal depends on temperature.
Thomson Effect is caused _______________ .
Metals are good conductor of heat than insulator because
- Consider circuit in figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the state of drift velocity?
- Electrons give up energy at the rate of RI2 per second to the thermal energy. What time scale would one associate with energy in problem (a)? n = no of electron/volume = 1029/m3, length of circuit = 10 cm, cross-section = A = (1mm)2
Derive an expression for resistivity of a conductor in terms of the number density of charge carriers in the conductor and relaxation time.
A potential difference (V) is applied across a conductor of length 'L' and cross-sectional area 'A'.
How will the drift velocity of electrons and the current density be affected if another identical conductor of the same material were connected in series with the first conductor? Justify your answers.
