8 Potentiometer

Potentiometer

Principle

When a constant current is passed through a wire of uniform area of cross-section, the potential drop across any portion of the wire is directly proportional to the length of that portion.

Construction

• Consists of a number of segments of wire of uniform area of cross-section
• Small vertical portions are made of thick metal strip connecting the various sections of wire.
• A rheostat is connected to the circuit, which can vary the amount of current flowing in the wire.

Applications of Potentiometer

• Comparison of emf of two cells

• E₁, E₂ are the emf of the two cells.
• 1, 2, 3 form a two way key.
• When 1 and 3 are connected, E₁ is connected to the galvanometer (G).
• Jokey is moved to N₁, which is at a distance l₁ from A, to find the balancing length.
• Applying loop rule to AN₁G31A,

Φ l₁ + 0 − E₁ = 0 (1)

Where, Φ is the potential drop per unit length

• Similarly, for E₂ balanced against l₂ (AN₂),

Φ l₂ + 0 −E₂ = 0 (2)

• From equations (1) and (2),

• Measures internal resistance of a cell

• The cell of emf E (internal resistance r) is connected across a resistance box (R) through key K₂.
• K₂ − open, balance length is obtained at length AN₁ = l₁

E= Φ l₁ (3)

• K₂ − closed
• Let V be the terminal potential difference of cell and the balance is obtained at AN₂ = l₂

∴ V = Φ l₂ (4)

From equations (3) and (4),

From (5) and (6),