Two cells of same emf E but internal resistance r₁ and r₂ are connected in series to an external resistor R (Fig 3.7). What should be the value of R so that the potential difference across the terminals of the first cell becomes zero.

Let there be n resistors R₁ ............R_n with R_max = max (R₁......... R_n) and R_min = min {R₁ ..... R_n}. Show that when they are connected in parallel, the resultant resistance R_P< R_min and when they are connected in series, the resultant resistance R_S > R_max. Interpret the result physically.

The circuit in Fig 3.6 shows two cells connected in opposition to each other. Cell E₁ is of emf 6V and internal resistance 2 Ω; the cell E₂ is of emf 4V and internal resistance 8Ω. Find the potential difference between the points A and B.

Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1mm. Conductor B is a hollow tube of outer diameter 2mm and inner diameter 1mm. Find the ratio of resistance R_A to R_B.

Suppose there is a circuit consisting of only resistances and batteries and we have to double (or increase it to n-times) all voltages and all resistances. Show that currents are unaltered. Do this for circuit of Example 3.7 in the NCERT Text Book for Class XII.