Two wires of equal diameters, of resistivities ρ₁ and ρ₂ and lengths l₁ and l₂, respectively, are joined in series. The equivalent resistivity of the combination is :

(1) $\frac{{\rho }_1{l}_1+{\rho }_2{l}_2}{l_1+l_2}$

(2) $\frac{{\rho }_1{l}_2+{\rho }_2{l}_1}{l_1-l_2}$

(3) $\frac{{\rho }_1{l}_2+{\rho }_2{l}_1}{l_1+l_2}$

(4) $\frac{{\rho }_1{l}_1-{\rho }_2{l}_2}{l_1-l_2}$ 

The resistance in the two arms of the balanced meter bridge as shown in figure are 5 and R, respectively. When the resistance R is shunted with an equal resistance, the new balance point is at 1.6l₁. The resistance 'R' is : 

1. 10

2. 15

3. 20 

4. 25

Three resistances P, Q, R each of 2Ω and an unknown resistance S form the four arms of a Wheatstone’s bridge circuit. When the resistance of 6 Ω is connected in parallel to S the bridge gets balanced. What is the value of S?

1. 2 $\Omega$

2. 3 $\Omega$

3. 6 $\Omega$

4. 1 $\Omega$ 

Six similar bulbs are connected as shown in the figure with a DC source of emf E and zero internal resistance.

The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be:

1. 2: 1

2. 4: 9

3. 9: 4

4. 1: 2

In a discharge tube ionization of enclosed gas is produced due to collisions between:

1. positive ions and neutral atoms/molecules

2. negative electrons and neutral atoms/molecules

3. photons and neutral atoms/molecules

4. neutral gas atoms/molecules

In the circuit shown cells, \(A\) and \(B\) have negligible resistance. For \(V_A =12 ~\text{V}\), \(R_1 = 500 ~\Omega \), and $\mathrm{}$\(R = 100 ~\Omega \) the galvanometer \((\text{G}) \) shows no deflection. The value of \(V_B\) is: 
     

1. \(4\) V
2. \(2\) V
3. \(12\) V
4. \(6\) V