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.

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

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

A battery of emf E and internal resistance, r, when connected with an external resistance of 12Ω produces a current of 0.5 A. When connected across a resistance of 25Ω, it produces a current of 0.25 A. Determine (i) the emf and (ii) the internal resistance of the cell.

A battery of emf 10 V and internal resistance 3 ohm is connected to a resistor. If the current in the circuit is 0.5 A, find : (i) the resistance of the resistor; (ii) the terminal voltage of the battery.

A cell of emf E and internal resistance r is connected to two external resistances R₁ and R₂ and a perfect ammeter. The current in the circuit is measured in four different situations : (i) without any external resistance in the circuit (ii) with resistance R1 only (iii) with R1 and R2 in series combination (iv) with R1 and R2 in parallel combination. The currents measured in the four cases are 0.42 A, 1.05 A, 1.4 A and 4.2 A, but not necessarily in that order. Identify the currents corresponding to the four cases mentioned above.

In the circuit shown in the figure, find the current through each resistor.

Derive the expression for the current density of a conductor in terms of the conductivity and applied electric field. Explain, with reason how the mobility of electrons in a conductor changes when the potential difference applied is doubled, keeping the temperature of the conductor constant.

What is relaxation time ? Derive an expression for resistivity of a wire in terms of number density of free electrons and relaxation time.

Two cells of emfs E₁ & E₂ and internal resistances r₁ & r₂ respectively are connected in parallel. Obtain expressions for the equivalent. (i) resistance and (ii) emf of the combination

First a set of n equal resistors of R each is connected in series to a battery of emf E and internal resistance R. A current I is observed to flow. Then the n resistors are connected in parallel to the same battery. It is observed that the current becomes 10 times. What is n ?

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) The potential difference applied across a given resistor is altered so that the heat produced per second increases by a factor of 9. By what factor does the applied potential difference change ? (ii) In the figure shown, an ammeter A and a resistor of 4 W are connected to the terminals of the source. The emf of the source is 12 V having an internal resistance of 2 W. Calculate the voltmeter and ammeter readings.

Define relaxation time of the free electrons drifting in a conductor. How is it related to the drift velocity of free electrons ? Use this relation to deduce the expression for the electrical resistivity of the material.