Current Electricity

The current density varies with radial distance r as J =ar² (where, a is a constant) in a  cylindrical wire of radius R. The current passing through the wire between radial distance $\frac{\mathrm{R}}{4}$ and $\frac{\mathrm{R}}{2}$ is 

• $\frac{20{\mathrm{\pi aR}}^4}{331}$

• $\frac{15{\mathrm{\pi aR}}^4}{512}$

• $\frac{{\mathrm{\pi aR}}^4}{332}$

• $\frac{3{\mathrm{\pi aR}}^4}{864}$

A thermister is dipped in a water bath. As the temperature increases the current in the thermistor also increases. This is due to decrease in

• resistivity

• conductivity

• reactance

• capacitance

In an AC circuit, voltage and current are given by V = 50 sin (lO0 t) V and I = 50 sin $\left(100 \mathrm{t} + \frac{\mathrm{\pi }}{3}\right)$ A. The power dissipiated in the circuit is

• 125 W

• 625 W

• 1250 W

• 100 W

Two electric bulbs rated 50W and 100W are glowing at full power, when used in parallel with a battery of emf 120 V and internal resistance 10 Ω. The maximum number of bulbs that can be connected in the circuit when glowing at full power is

• 6

• 4

• 2

• 8

A resistance of 4 Ω and a wire of length 5 m and resistance 5 Ω are joined in series and connected to a cell of emf 10 V and internal resistance of 1 Ω. A parallel combination of two identical cells in balanced across 3 m of the wire. The emf E of each cell is

• 1.5 V

• 3.0 V

• 0.67 V

• 1.33 V

Two straight infinitely long current carrying wires are kept along Z-axis at the co-ordinates (0, a, O) and (0, -a, 0) respectively, as shown in figure. The current in each of the wire is equal and along negative Z-axis (into the plane of the paper).

The variation of magnetic field on the X-axis will be approximately

The co-ordinates of centre of mass of the uniform lamina shown in figure, is if smal disc of radius $\frac{\mathrm{a}}{2}$  is cut from disc of radius a

• $\left(\frac{\mathrm{a}}{6} , \frac{\mathrm{a}}{6}\right)$

• $\left(\frac{\mathrm{a}}{6} , 0\right)$

• $\left(\mathrm{o} , \frac{-\mathrm{a}}{6}\right)$

• $\left(\frac{-\mathrm{a}}{6} , 0\right)$

When a battery connected across a resistor of 16Ω, the voltage across the resistor is 12 V. When the same battery is connected across itt hen the voltage is 11 V. The internal
resistance of the battery (in ohm) is

• $\frac{10}{7}$

• $\frac{20}{7}$

• $\frac{25}{7}$

• $\frac{30}{7}$

The total current supplied to the given circuit is

• 9 A

• 6 A

• 2 A

• 4 A

At room temperature, copper has free electron density of 8.4 x 1028 m^-3 . The electron drift velocity in a copper conductor of cross-sectional area of 10^-6 m² ? and carrying a current of 5.4 A, will be

• 4 ms^-1

• 0.4 ms^-1

• 4 cm s^-1

• 0.4 mm s^-1