(i) Derive an expression for drift velocity of electrons in a conductor. Hence deduce Ohm’s law.
(ii) A wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts. Which of the following quantities remain constant in the wire ?
(a) drift speed
(b) current density
(c) electric current
(d) electric field
Justify your answer.
(ii) A wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts. Which of the following quantities remain constant in the wire ?
(a) drift speed
(b) current density
(c) electric current
(d) electric field
Justify your answer.
Two metallic wires P₁ and P₂ of the same material and same length but different cross-sectional areas A₁ and A₂ are joined together and then connected to a source of emf. Find the ratio of the drift velocities of free electrons in the wires P₁ and P₂ if the wires are connected
(i) in series, and (ii) in parallel.
(a) Define the term ‘conductivity’ of a metallic wire. Write its SI unit.
(b) Using the concept of free electrons in a conductor, derive the expression for the conductivity of a wire in terms of number density and relaxation time. Hence obtain the relation between current density and the applied electric field E.
Derive the expression for the current density of a conductor in terms of the conductivity and applied electric field. Explain, with reason how the mobility of electrons in a conductor changes when the potential difference applied is doubled, keeping the temperature of the conductor constant.
(i) Derive an expression for drift velocity of free electrons.
(ii) How does drift velocity of electrons in a metallic conductor vary with increase in temperature ? Explain.
Define the term current density of a metallic conductor. Deduce the relation connecting current density (J) and the conductivity σ of the conductor, when an electric field E, is applied to it.
A wire of resistance 0.5 Ωm⁻¹ is bent into a circle of radius 1m. The same wire is connected across a diameter AB as shown in the fig. The equivalent resistance is
(a) Π ohm
(b) Π (Π + 2) ohm
(c) Π/( Π + 4) ohm
(d) (Π + 1) ohm
Draw a plot showing the variation of resistivity of a (i) conductor and (ii) semiconductor, with the increase in temperature. How does one explain this behaviour in terms of number density of charge carriers and the relaxation time ?
(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase : current or voltage ?
(ii) Without making any other change, find the value of the additional capacitor C₁, to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.
The potential difference across a resistor ‘r’ carrying current ‘I’ is Ir.
(i) Now if the potential difference across ‘r’ is measured using a voltmeter of resistance ‘’, show that the reading of voltmeter is less than the true value.
(ii) Find the percentage error in measuring the potential difference by a voltmeter.
(iii) At what value of ’, does the voltmeter measures the true potential difference?
Define relaxation time of the free electrons drifting in a conductor. How is it related to the drift velocity of free electrons ? Use this relation to deduce the expression for the electrical resistivity of the material.
Two thin concentric and coplanar spherical shells, of radii a and b (b > a) carry charges, q and Q, respectively. Find the magnitude of the electric field, at a point at distance x, from their common centre for :
(i) 0 < x < a
(ii) a x < b
(iii) b x <
A source of ac voltage V = V₀ sin ωt is connected to a series combination of a resistor ‘R’ and a capacitor ‘C’. Draw the phasor diagram and use it to obtain the expression for
(i) impedance of the circuit and
(ii) phase angle.
A circuit containing an 80 mH inductor and a 250 µF capacitor in series connected to a 240 V,100 rad/s supply. The resistance of the circuit is negligible.
(i) Obtain rms value of current.
(ii) What is the total average power consumed by the circuit ?
Two cells of emfs E₁ & E₂ and internal resistances r₁ & r₂ respectively are connected in parallel. Obtain expressions for the equivalent.
(i) resistance and
(ii) emf of the combination