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

Four resistances of 100 Ω each are connected in the form of square. Then, the effective resistance along the diagonal points is :

(1) 200 Ω

(2) 400 Ω

(3) 100 Ω

(4) 150 Ω

Equivalent resistance between the points A and B is (in Ω) 

(1) $\frac{1}{5}$

(2) $1\frac{1}{4}$

(3) $2\frac{1}{3}$

(4) $3\frac{1}{2}$

In the circuit shown here, what is the value of the unknown resistor R so that the total resistance of the circuit between points P and Q is also equal to R 

(1) 3 ohms

(2) $\sqrt{39}ohms$

(3) $\sqrt{69}ohms$

(4) 10 ohms

The resistors of resistances 2 Ω, 4 Ω and 8 Ω are connected in parallel, then the equivalent resistance of the combination will be :

(1) $\frac{8}{7}\Omega$

(2) $\frac{7}{8}\Omega$

(3) $\frac{7}{4}\Omega$

(4) $\frac{4}{9}\Omega$ 

In the circuit, the potential difference across PQ will be nearest to 

(1) 9.6 V

(2) 6.6 V

(3) 4.8 V

(4) 3.2 V

Three resistors are connected to form the sides of a triangle ABC, the resistance of the sides AB, BC and CA are 40 ohms, 60 ohms and 100 ohms respectively. The effective resistance between the points A and B in ohms will be 

(1) 32

(2) 64

(3) 50

(4) 200

Equivalent resistance across terminals \(A\) and \(B\) will be:

Two wires of the same dimensions but resistivities ρ₁ and ρ₂ are connected in series. The equivalent resistivity of the combination is 

(1) ρ₁ + ρ₂

(2) $\frac{{\rho }_1+{\rho }_2}{2}$

(3) $\sqrt{{\rho }_1{\rho }_2}$

(4) $2({\rho }_1+{\rho }_2)$

A 3 volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current I, in the circuit will be 

(1) 1/3 A

(2) 1 A

(3) 1.5 A

(4) 2 A