(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.
(ii) How does drift velocity of electrons in a metallic conductor vary with increase in temperature ? Explain.
(i) When a potential difference is applied across a conductor, an electric field is produced and free electrons are acted upon by an electric force ( = –Ee). Due to this, electrons accelerate and keep colliding with each other and acquire a constant (average) velocity , which is known as drift velocity.
(ii) Decreases, as time of relaxation decreases.
(ii) Decreases, as time of relaxation decreases.
Write the expression for the drift velocity of charge carriers in a conductor of length l across which a potential difference V is applied.
How does one explain increase in resistivity of a metal with increase in temperature ?
Using the concept of drift velocity of charge carriers in a conductor, deduce the relationship between current density and resistivity of the conductor.
How does the random motion of free electrons in a conductor get affected when a potential difference is applied across its ends ?
What is relaxation time ? Derive an expression for resistivity of a wire in terms of number density of free electrons and relaxation time.
Show that in the free oscillations of an LC circuit, the sum of energies stored in the capacitor and the inductor is constant in time.
A sinusoidal voltage of peak value 10 V is applied to a series LCR circuit in which resistance,capacitance and inductance have values of 10 Ω,1 µF and 1 H respectively. Find
(i) the peak voltage across the inductor at resonance
(ii) quality factor of the circuit.
Derive the expression for the average power dissipated in a series LCR circuit for an ac source of a voltage, V = sin ωt , carrying a current,i = sin (ωt + Φ)
Hence define the term “Wattless current”. State under what condition it can be realized in a circuit.
(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.
Derive an expression for electric field of a dipole at a point on the equatorial plane of the dipole. How does the field vary at large distances?
An inductor of 200 mH, capacitor of 400 µF and a resistor of 10 Ω are connected in series to ac source of 50 V of variable frequency. Calculate the
(a) angular frequency at which maximum power dissipation occurs in the circuit and the corresponding value of the effective current, and
(b) value of Q-factor in the circuit.
(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.