In a series LCR circuit, obtain the conditions under which
(i) the impedance of the circuit is minimum, and
(ii) wattless current flows in the circuit.
A 40 mF capacitor is connected to a 200 V, 50 Hz ac supply. The r.m.s value of the current in the circuit is, nearly
(a) 1.7 A
(b) 2.05 A
(c) 2.5 A
(d) 25.1 A
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.
An alternating voltage given by V = 140sin314 t is connected across a pure resistor of 50 Find :
(i) the frequency of the source.
(ii) the rms current through the resistor.
In highly inductive load circuit, it is more dangerous when
(a) we close the switch
(b) open the switch
(c) increasing the resistance
(d) decreasing the resistance
A lamp is connected in series with a capacitor. Predict your observation for dc and ac connections. What happens in each if the capacitance of the capacitor is reduced ?
A source of ac voltage V = V₀ sin ωt, is connected across a pure inductor of inductance L. Derive the expressions for the instantaneous current in the circuit. Show that average power dissipated in the circuit is zero.
A cell of emf 4 V and internal resistance 1 W is connected to a d.c. source of 10 V through a resistor of 5 W. Calculate the terminal voltage across the cell during charging.
Two cells of E.M.F. 10 V and 2 V and internal resistances 10 Ω and 5 Ω respectively, are connected in parallel as shown. Find the effective voltage across R.
Two electric bulbs P and Q have their resistances in the ratio of 1 : 2. They are connected in series across a battery. Find the ratio of the power dissipation in these bulbs.
Using the concept of drift velocity of charge carriers in a conductor, deduce the relationship between current density and resistivity of the conductor.
A lamp is connected in series with a capacitor. Predict your observation for dc and ac connections. What happens in each if the capacitance of the capacitor is reduced ?
Two closely spaced equipotential surfaces A and B with potentials V and V + , (where is the change in V), are kept distance apart as shown in the figure. Deduce the relation between the electric field and the potential gradient between them. Write the two important conclusions concerning the relation between the electric field and electric potentials.
N spherical droplets, each of radius r, have been charged to have a potential V each. If all these droplets were to coalesce to form a single large drop, what would be the potential of this large drop ?
(It is given that the capacitance of a sphere of radius x equals