Current Electricity

A copper wire of cross-sectional area 1 × 10⁻⁶ m² carries a current of 1.6 A. If the free-electron density is 8 × 10²⁸ /m³, find the drift velocity of the electrons. (e = 1.6 × 10⁻¹⁹ C)

A wire of circular cross-section has radius 1 mm and carries a steady current of 3.14 A. Find the current density in the wire. (Take π ≈ 3.14)

A cell of emf 3 V is balanced against a length of 1.5 m on a potentiometer wire carrying a steady current. What is the potential gradient along the wire?

A wire of resistivity 1.1 × 10⁻⁶ Ω·m has length 2 m and cross-sectional area 2.2 × 10⁻⁷ m². Find its resistance.

A wire of resistance R is uniformly stretched, without changing its volume, until its length becomes 3 times the original length. What is its new resistance?

The length of a wire of resistance 50 Ω is increased by 2% by stretching, without changing its volume. Find the new resistance.

A heating element has resistance 20 Ω at 0°C and a temperature coefficient of resistance α = 2 × 10⁻³ °C⁻¹. At what temperature will its resistance become 30 Ω?

A carbon resistor has the colour bands Brown, Black, Red, Gold (in that order). What is its resistance value and tolerance?

Three resistors of 2 Ω, 3 Ω, and 6 Ω are connected in parallel. Find the equivalent resistance.

At a circuit junction, currents of 5 A and 3 A flow in. Two currents, I and 2 A, flow out. Find I.

A battery of emf 12 V and internal resistance 1 Ω is connected to an external resistor of 5 Ω. Find the terminal voltage of the battery.

Four identical cells, each of emf 1.5 V and internal resistance 0.5 Ω, are connected in series to an external resistance of 4 Ω. Find the current in the circuit.

Three identical cells, each of emf 2 V and internal resistance 3 Ω, are connected in parallel to an external resistance of 1 Ω. Find the current delivered to the external resistor.

An electric heater rated 1000 W operates for 2 hours daily. At ₹6 per unit (kWh), find the cost of running it for one day.

A cell of emf 10 V and internal resistance 2 Ω is connected to a variable external resistance R. Find the value of R for which the power delivered to R is maximum, and the value of that maximum power.

Two bulbs, rated 100 W and 60 W (both at 220 V), are connected in series to a 220 V supply. Which bulb glows brighter, and why?

A galvanometer of resistance 99 Ω requires a current of 10 mA for full-scale deflection. What shunt resistance is needed to convert it into an ammeter of range 1 A?

In a Wheatstone bridge, the four arms have resistances P = 4 Ω, Q = 6 Ω, and R = 10 Ω. Find the value of S for the bridge to be balanced.