Show that the current leads the voltage in phase by in an ac circuit containing an ideal capacitor.
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.
In electric arc furnace Cu or Iron is melted due to variation of
(a) current
(b) magnetic field
(c) voltage
(d) electric field
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?
(i) When an ac source is connected to an ideal capacitor show that the average power supplied by the source over a complete cycle is zero.
(ii) A lamp is connected in series with a capacitor.Predict your observation when the system is connected first across a dc and then an ac source.What happens in each case if the capacitance of the capacitor is reduced ?
(i) Deduce the relation between current I flowing through a conductor and drift velocity of the electrons.
(ii) Figure shows a plot of current ‘I’ flowing through the cross-section of a wire versus the time ‘t’. Use the plot to find the charge flowing in 10 s through the wire.
An inductor L of inductance is connected in series with a bulb B and an ac source. How would brightness of the bulb change when
(i) number of turns in the inductor is reduced,
(ii) an iron rod is inserted in the inductor and
(iii) a capacitor of reactance is inserted in series in the circuit. Justify your answer in each case.
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 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 <
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.