The length of a wire of a potentiometer is \(100~\text{cm}\), and the emf of its standard cell is \(E\) volt. It is employed to measure the emf of a battery whose internal resistance is \(0.5~\Omega\). If the balance point is obtained at \(l = 30~\text{cm}\) from the positive end, the emf of the battery is:
1. \(\frac{30E}{100}\)
2. \(\frac{30E}{100.5}\)
3. \(\frac{30E}{(100-0.5)}\)
4. \(\frac{30(E-0.5i)}{100}, \) where \(i\) is the current in the potentiometer

What is the reading of the voltmeter in the following figure?

(1) 3 V

(2) 2 V

(3) 5 V

(4) 4 V

In a metre bridge experiment, the null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X against Y 

(1) 50 cm

(2) 80 cm

(3) 40 cm

(4) 70 cm

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