Potentiometer wire of length 1 m is connected in series with 490 Ω resistance and 2V battery. If 0.2 mV/cm is the potential gradient, then the resistance of the potentiometer wire is :

(1) 4.9 Ω

(2) 7.9 Ω

(3) 5.9 Ω

(4) 6.9 Ω

In an electrical cable, there is a single wire of radius 9 mm of copper. Its resistance is 5 Ω. The cable is replaced by 6 different insulated copper wires, the radius of each wire is 3 mm. Now the total resistance of the cable will be :

(1) 7.5 Ω

(2) 45 Ω

(3) 90 Ω

(4) 270 Ω

Two uniform wires A and B are of the same metal and have equal masses. The radius of wire A is twice that of wire B. The total resistance of A and B when connected in parallel is :

(1) 4 Ω when the resistance of wire A is 4.25 Ω

(2) 5 Ω when the resistance of wire A is 4.25 Ω

(3) 4 Ω when the resistance of wire B is 4.25 Ω

(4) 7 Ω when the resistance of wire B is 4.25 Ω

Twelve wires of equal length and same cross-section are connected in the form of a cube. If the resistance of each of the wires is \(R\), The effective resistance between two diagonal ends \(A\) and \(E\) will be:

1. \(2R\)
2. \(12R\)
3. \(\frac{5}{6}R\)
4. \(8R\)

You are given several identical resistances each of value R = 10 Ω and each capable of carrying maximum current of 1 ampere. It is required to make a suitable combination of these resistances to produce a resistance of 5 Ω which can carry a current of 4 amperes. The minimum number of resistances of the type R that will be required for this job 

(1) 4

(2) 10

(3) 8

(4) 20

The resistance of a wire is 10^–6 Ω per metre. It is bend in the form of a circle of diameter 2 m. A wire of the same material is connected across its diameter. The total resistance across its diameter AB will be

(1) $\frac{4}{3}\pi \times {10}^{-6}\Omega$

(2) $\frac{2}{3}\pi \times {10}^{-6}\Omega$

(3) $0.88\times {10}^{-6}\Omega$

(4) $14\pi \times {10}^{-6}\Omega$

In the figure shown, the capacity of the condenser C is $2\mu F$. The current in 2 Ω resistor is : 

(1) 9 A

(2) 0.9 A

(3) $\frac{1}{9}A$

(4) $\frac{1}{0.9}A$

When the key K is pressed at time t = 0, which of the following statements about the current I in the resistor AB of the given circuit is true?

(1) I = 2 mA at all t

(2) I oscillate between 1 mA and 2mA

(3) I = 1 mA at all t

(4) At t = 0 , I = 2 mA and with time it goes to 1 mA

A torch bulb rated as 4.5 W, 1.5 V is connected as shown in the figure. The e.m.f. of the cell needed to make the bulb glow at full intensity is :

(1) 4.5 V

(2) 1.5 V

(3) 2.67 V

(4) 13.5 V

In the circuit shown in the figure, the current through :

1. The 3Ω resistor is 0.50A

2. The 3Ω resistor is 0.25 A

3. The 4Ω resistor is 0.50A

4. The 4Ω resistor is 0.25 A