Question

Five cells each of emf E and internal resistance r send the same amount of current through an external resistance R whether the cells are connected in parallel or in series. Then the ratio `("R"/"r")` is:

विकल्प

• 2

• `1/2`

• `1/5`

• 1

Answer 1

1

Explanation:

Given: Number of cells, n = 5, emf of each cell = E

Internal resistance of each cell = r

In series, current through resistance R

I = `"nE"/("nr" + "R") = (5"E")/(5"r" + "R")`

In parallel, current through resistance R

I' = `"E"/("r"/"n" + "R") = "nE"/("r" + "nR") = (5"E")/("r" + 5"R")`

According to question, I = I'

∴ `(5"E")/(5"r" + 5"R") = (5"E")/("r" + 5"R")`

⇒ 5r + R = r + 5R

or R = r

∴ `"R"/"r"` = 1