Question

Three cells of emf E, 2E and 5E having internal resistances r, 2r and 3r respectively are connected across a variable resistance R as shown in the figure. Find the expression for the current. Plot a graph for variation of current with R.

Answer 1

Here, E₁ = E, E₂ = – 2E and E₃ = 5E, r₁ = r,r₂ = 2r and r₃ = 3r Equivalent emf of the cell is E = E₁ + E₂ + E₃

= E – 2E + 5E = 4E

Equivalent resistance

= r₁ + r₂ + r₃ + R

= r + 2r + 3r + R = 6r + R

∴ Current, I = \(\frac{4E}{6r+R}\)

The graph for variation of current I with resistance R is shown above.