(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.
(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.
(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 ?
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 voltage V = V₀ sin ωt is applied to a series LCR circuit. Derive the expression for the average power dissipate over a cycle.Under what conditions is
(i) no power dissipated even though the current flows through the circuit,
(ii)maximum power dissipated in the circuit ?
A device ‘X’ is connected to an ac source V = V₀ sin(ωt). The variation of voltage, current and power in one complete cycle is shown in the following figure.
(i) Which curve shows power consumption over a full cycle?
(ii) Identify the device ‘X’.
The core of a transformer is laminated because
(a) ratio of voltage in primary and secondary may be increased
(b) energy losses due to eddy currents may be minimized
(c) the weight of the transformer may be reduced
(d) rusting of the core may be prevented
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 ?
The following table gives the length of three copper wires, their diameters, and the applied potential difference across their ends. Arrange the wires in increasing order according to the following :
(i) The magnitude of the electric field within them,
(ii) The drift speed of electrons through them, and
(iii) The current density within them.
(i) Write two properties by which electric potential is related to the electric field.
(ii) Two point charges q₁ and q₂ separated by a distance of r₁₂ are kept in an external electric field. Derive an expression for the potential energy of the system of two charges in the field.
The current, in the LCR circuit shown in the figure is observed to lead the voltage in phase. Without making any other change in the circuit, a capacitor,of capacitance C₀, is (appropriately) joined to the capacitor C. This results in making the current,in the ‘modified’ circuit, flow in phase with theapplied voltage.
Draw a diagram of the ‘modified’ circuit and obtain an expression for C₀ in terms of ω, L and C.
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).
A charge + Q, is uniformly distributed within a sphere of radius R. Find the electric field, due to this charge distribution, at a distant point r from the centre of the sphere where :
(i) 0 < r < R
(ii) r > R
(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.