Question

Which of the following equations gives correct expression for the internal resistance of a cell by using potentiometer?

पर्याय

• `r = R [V/E - 1]`

• `r = R [1 - E/V]`

• `r = R [1 - V/E]`

• `r = R [E/V - 1]`

Answer 1

`bb(r = R [E/V - 1])`

Explanation:

The internal resistance of a cell can be derived using Ohm’s law and the potentiometer principle.

Let,

E = EMF of the cell (when no current is drawn)

V = Terminal voltage of the cell (when current flows)

R = External resistance in the circuit

r = Internal resistance of the cell

Using the relation between EMF, terminal voltage, and internal resistance:

E = V + Ir

where I is the current in the circuit.

Since I = `V/R`​ (from Ohm’s law), substituting in the equation:

E = `V + V/R r`

Rearranging for r:

r = `R [E/V - 1]`