In given figure, the potentiometer wire AB has a resistance of 5 Ω and length 10 m. The balancing length AM for the emf of 0.4 V is :

1. 0.4 m

2. 4 m

3. 0.8 m

4. 8 m

If the resistance of voltmeter is 10000Ω and resistance of ammeter is 2Ω then find R when voltmeter reads 12V and ammeter reads 0.1 A :

1. 118 Ω

2. 120 Ω

3. 124 Ω

4. 114Ω

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