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 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.
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 200 mH (pure) inductor and a 5 µF (pure) capacitor are connected one by one, across a sinusoidal ac voltage source of V = [70.7sin (1000t)] voltage. Obtain the expression for the current in each case.
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.
An ac voltage V = V₀ sin ωt is applied to a pure inductor L. Obtain an expression for the current in the circuit. Prove that the average power supplied to an inductor over one complete cycle is zero.
High voltage transmission line is preferred as
(a) Its appliances are less costly
(b) Thin power cables are required
(c) Idle current very low
(d) Power loss is very less
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.
(i) When an ac source is connected to an ideal inductor shows that the average power supplied by the source over a complete cycle is zero.
(ii) A lamp is connected in series with an inductor and an ac source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the inductor ? Explain.
A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and
(ii) the current I.
It is found that when R = 4 Ω, the current is 1 A when R is increased to 9 Ω, the current reduces to 0.5 A. Find the values of the emf E and internal resistance r.
A particle, having a charge +5 µC, is initially at rest at the point x = 30 cm on the x-axis. The particle begins to move due to the presence of a charge Q that is kept fixed at the origin. Find the kinetic energy of the particle at the instant it has moved 15 cm from its initial position if
(a) Q = +15 µC and
(b) Q = – 15 µC
In the two electric circuits shown in the figure, determine the readings of ideal ammeter (A) and the ideal voltmeter (V).
(i) Derive the expression for the electric potential due to an electric dipole at a point on its axial line.
(ii) Depict the equipotential surface due to electric dipole.
(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.