An alternating voltage E = E₀ sin ωt is applied to the circuit containing a resistor R connected in series with a black box. The current in the circuit is found to be I=I₀ (sin ωt+π/4)

Calculate the current drawn from the battery by the network of resistors shown in the figure.

Draw a graph showing variation of resistivity with temperature for nichrome. Which property of nichrome is used to make standard resistance coils ?

Draw a plot showing the variation of resistivity of a (i) conductor and (ii) semiconductor, with the increase in temperature. How does one explain this behaviour in terms of number density of charge carriers and the relaxation time ?

Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 2.5 × 10⁻⁷ m² carrying a current of 1.8 A. Assume the density of conduction electrons to be 9 × 10²⁸ m⁻³.

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.

In the circuit shown in the figure, find the total resistance of the circuit and the current in the arm CD.

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 cells of emf $E_{1}$ and $E_{2}$ have internal resistance $r_{1}$ and $r_{2}$. Deduce an expression for equivalent emf of their parallel combination.

Two cells of emfs 1.5 V and 2.0 V having internal resistances 0.2Ω and 0.3Ω respectively are connected in parallel. Calculate the emf and internal resistance of the equivalent cell.

Using the concept of drift velocity of charge carriers in a conductor, deduce the relationship between current density and resistivity of the conductor.

A 9 V battery is connected in series with a resistor. The terminal voltage is found to be 8 V. Current through the circuit is measured as 5 A. What is the internal resistance of the battery?

Distinguish between emf (E) and terminal voltage (V) of a cell having internal resistance r. Draw a plot showing the variation of terminal voltage (V) Vs. the current (I) drawn from the cell. Using this plot, how does one determine the internal resistance of the cell ?

The figure shows a plot of terminal voltage ‘V’ versus the current ‘i’ of a given cell. Calculate from the graph (i) emf of the cell and (ii) internal resistance of the cell.

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.