The equivalent resistance between the points P and Q in the network given here is equal to (given $r=\frac{3}{2}\Omega$) :

(1) $\frac{1}{2}\Omega$

(2) 1 Ω

(3) $\frac{3}{2}\Omega$

(4) 2 Ω

In the adjoining circuit, the battery E₁ has an e.m.f. of 12 volts and zero internal resistance while the battery E has an e.m.f. of 2 volts. If the galvanometer G reads zero, then the value of the resistance X in ohm is 

(1) 10

(2) 100

(3) 500

(4) 200

Five resistances are connected as shown in the figure. The effective resistance between the points A and B is :

(1) $\frac{10}{3}\Omega$

(2) $\frac{20}{3}\Omega$

(3) 15 Ω

(4) 6 Ω

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

Masses of three wires of copper are in the ratio of 1 : 3 : 5 and their lengths are in the ratio of 5 : 3 : 1. The ratio of their electrical resistances are :

(1) 1 : 3 : 5

(2) 5 : 3 : 1

(3) 1 : 15 : 125

(4) 125: 15: 1

The drift velocity of the electrons in a current-carrying  metallic conductor is of the order of 

1.  ${10}^4 \mathrm{m}/\mathrm{s}$

2.  ${10}^8 \mathrm{m}/\mathrm{s}$

3.  ${10}^0\mathrm{m}/\mathrm{s}$

4.  ${10}^{-4}\mathrm{m}/\mathrm{s}$

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

A battery consists of a variable number 'n' of identical cells having internal resistances connected in series. The terminals of battery are short circuited and the current i is measured. Which of the graph below shows the relation ship between i and n

(1)

(2)

(3)

(4)

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

A wire of resistance R is cut into ‘n’ equal parts. These parts are then connected in parallel. The equivalent resistance of the combination will be :

(1) nR

(2) $\frac{R}{n}$

(3) $\frac{n}{R}$

(4) $\frac{R}{n^2}$