A metallic wire having resistivity ρ is cut into four equal parts. The resistivity of each part is:

Consider two cells of emf $$ε_1$$​ and $$ε_2$$​ with internal resistances $$г_1$$​ and $$г_2$$​, respectively. The two cells are connected in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is equivalent to a single cell with emf given by:

Consider a potentiometer set-up where a cell of emf 2.25 V gives a balance point at 63.0 cm length of the wire. Now the cell is replaced by another cell and the balance point shifts to 21.0 cm. Then the emf of the second cell is:

Two resistors $$R_1$$​ and $$R_2$$​ have their resistance values in the ratio of 3 : 5. When they are combined in series, their equivalent resistance is 24 Ω. The individual resistances $$R_1$$​ and $$R_2$$​, respectively, are:

Suppose you mention the resistivity of an alloy as $$R_{alloy}$$​ which is made of two metals, A and B, and the resistivity of the constituent metals are denoted by $$R_A$$​ and $$R_B$$​. Which of the following relations is true?

A potentiometer wire of length 100 cm has a resistance of 30 ohms. It is connected in series with a resistance of 20 ohms and an accumulator of emf 10 V having negligible internal resistance. A source of 2.4 V is balanced against a length L of the potentiometer wire. What is the value of L?

Two batteries $$\text{E}_1$$​ (emf: 6V, internal resistance: 0.5 Ω) and $$\text{E}_2$$​ (emf: 12V, internal resistance: 1.0 Ω) are connected in parallel by connecting their positive terminals to point A and negative terminals to point B. A third battery $$\text{E}_3$$​ [emf: 6V, internal resistance: ($$\frac{2}{3}$$​) Ω] is connected in series with this combination by connecting its positive terminal to B. The equivalent emf of this combination is

Three resistors $$\text R_1,\text R_2$$​ and $$\text R_3$$​ have their resistance values in the ratio of 2 : 3 : 4. They are combined in parallel and their equivalent resistance is 24 Ω. Then the individual resistances $$\text R_1,\text R_2$$​ and $$\text R_3$$​ are:

A copper wire of uniform area of cross-section $$3.4×10^{-5}\space\text m^2$$​ carries a current of 4.0 A. The magnitude of the electric field applied is ____________ (Resistivity of copper: $$1.7×10^{-8}$$​ Ω m).

The intercept of the y-axis for the graph between stopping potential versus frequency will give us:

Two batteries, $$\text E_1$$​ (emf: 3 V, internal resistance: 0.5 Ω) and $$\text E_2$$​ (emf: 6 V, internal resistance: 1.0 Ω), are connected in series by connecting the positive terminal of $$\text E_2$$​ to the negative terminal of $$\text E_1$$. A third battery $$\text E_3$$​ (emf: 6 V, internal resistance: 1.0 Ω) is connected in parallel with this combination by connecting its positive terminal to the positive terminal of $$\text E_1$$​ and its negative terminal to the negative terminal $$\text E_2$$​. The equivalent emf of this combination is: