Question

A long resistance wire is stretched between two iron nails. A battery of 2V is applied across the wire. One end of a torch bulb is connected to nail and other end is made in contact as shown in figure.

1. If this wire slides over the resistance wire from nail 1 to nail 2, what happens to the brightness of the bulb.

• Increases 
• Decreases 
• Remains constant 
• First increases then decreases. 

2. How this principle is used to determine internal resistance of cell.

3. What happens to the reading, if we change 2V with 3V during the time of reading

Answer 1

1. Increases.

2. Measurement of internal resistance using potentiometer

Principle: [Same as before]

a. Circuit details : Battery B₁ Rheostat and key K₁ are connected in between A and B. This circuit is called primary.

In the secondary circuit a battery E having internal resistance ‘r’ is connected. A resistance box (R) is connected across the battery through a key (K₂). Jockey is connected to battery through galvanometer.

b. Working and theory :

The key (K₁) in the primary circuit is closed and the key is the secondary (K₂) is open. Jockey is moved to get zero deflection in galvanometer. The balancing length l₁ , (from A) is found out. Then we can write.

E₁ ∝ I₁ .......(1)

Key K₂ is put in the circuit, corresponding balancing length (I₂) is found out. Let V be the applied voltage, then

V₁ ∝ I₁ ......... (2)

‘V’ is the voltage across resistance box. Current through resistance box ie, voltage across resistance,

V = \(\frac{ER}{(R+r)}\) ......(3)

V = \(\frac{ER}{(R+r)}∝I_2\) ........(4)

Dividing eq (1) by eq (4),

\(\frac{E}{\frac{ER}{(R +r)}}=\frac{l_1}{l_2}\)       \(\frac{R+r}{R}=\frac{l_1}{l_2}\)

r = \(\frac{R(l_1-l_2)}{l_2}\)

3. Primary Voltage should not change while doing experiment. When we use 3v instead of 2v, potential gradient will change. Hence balancing length will change.