Advertisements
Advertisements
प्रश्न
- 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
Advertisements
उत्तर
a. Relation between current and drift velocity is given by I = ne Avd, where vd is the drift speed of electrons and n is the number density of electrons.
According to the Ohm's law current in the circuit
I = V/R
I = 6 V/6 Ω = 1 A
But, I = ne Avd
or vd = `I/("ne A")`
On substituting the values,
For, n = number of electrons/volume = 1029/m3
Length of circuit = 10 cm, cross-section = A = (1 mm)2
`v_d = 1/(10^29 xx 16 xx 10^-19 xx 10^-6)`
= `1/1.6 xx 10^-4` m/s
Therefore, the energy absorbed in the form of KE is given by
Total KE = KE of 1 electron × no. of electrons
KE = `1/2 m_e v_d^2 xx n Al`
= `1/2 xx 9.1 xx 10^31 xx 1/2.56 xx 10^-8 xx 10^29 xx 10^-6 xx 10^-1`
= `2 xx 10^-17 J`
b. Ohmic loss (power loss) is `P = I^2R = 6 xx 1^2 = 6 W = 6 J/s`
Since, the energy dissipated per unit time is the power dissipated.
So, `P = E/t`
Therefore, `E = P xx t`
or `t = E/P = (2 xx 10^17)/6 = 10^17 s`
Important point: The energy dissipated per unit time is the power dissipated `P = (ΔW)/(Δt)`
The power across a resistor is P = I2R.
APPEARS IN
संबंधित प्रश्न
Write its (‘mobility’ of charge carriers) S.I. unit
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 1.8 A. Assume the density of conduction electrons to be 9 × 1028 m−3.
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
The number density of free electrons in a copper conductor is 8.5 × 1028 m−3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 × 10−6 m2 and it is carrying a current of 3.0 A.
How does drift velocity of electrons in a metallic conductor vary with increase in temperature? Explain.
On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time. On what factors does resistivity of a conductor depend?
Explain the term ‘drift velocity’ of electrons in conductor. Hence obtain the expression for the current through a conductor in terms of ‘drift velocity’.
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?
Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.
Electrons are emitted by a hot filament and are accelerated by an electric field, as shown in the figure. The two stops at the left ensure that the electron beam has a uniform cross-section.
A current of 1.0 A exists in a copper wire of cross-section 1.0 mm2. Assuming one free electron per atom, calculate the drift speed of the free electrons in the wire. The density of copper is 9000 kg m–3.
Consider a wire of length 4 m and cross-sectional area 1 mm2 carrying a current of 2 A. If each cubic metre of the material contains 1029 free electrons, find the average time taken by an electron to cross the length of the wire.
Consider the following statements.
(A) Free-electron density is different in different metals.
(B) Free-electron density in a metal depends on temperature.
Seebeck Effect is caused _____________ .
Amount of charge in coulomb required to deposit one gram equivalent of substance by electrolysis is:-
The drift velocity of a free electron inside a conductor is ______
The identical conductors maintained at same temperature are given potential difference in the ratio 1 : 2. Then the ratio of their drift velocities is ______.
Is the momentum conserved when charge crosses a junction in an electric circuit? Why or why not?
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.
The drift velocity of electrons in a conductor connected to a battery is given by vd = `(−"eE" τ)/"m"`. Here, e is the charge of the electron, E is the electric field, τ is the average time between collisions and m is the mass of the electron.
Based on this, answer the following:
- How does the drift velocity change with a change in the potential difference across the conductor?
- A copper wire of length 'l' is connected to a source. If the copper wire is replaced by another copper wire of the same area of cross-section but of length '4l', how will the drift velocity change? Explain your answer.
