In metre bridge experiment, with a standard resistance in the right gap and a resistance coil dipped in water (in a beaker) in the left gap, the balancing length obtained is '1'. If the temperature of water is increased, the new balancing

Options

A. ` lt l`
B. ` gt l`
C. ` = 0 `
D. `=l`

Answer

To solve the problem regarding the meter bridge experiment, we will follow these steps:

### Step 1: Understand the Initial Setup
In the meter bridge experiment, we have a standard resistance \( R \) on one side (right gap) and a resistance coil \( X \) dipped in water on the other side (left gap). The initial balancing length obtained is \( L \).

### Step 2: Apply the Principle of the Meter Bridge
According to the principle of the meter bridge (which is based on the Wheatstone bridge principle), the balancing condition is given by:
\[ \frac{X}{R} = \frac{L}{100 - L} \]
Here, \( L \) is the length of the bridge corresponding to the resistance \( X \), and \( 100 - L \) corresponds to the resistance \( R \).

### Step 3: Consider the Effect of Temperature on Resistance
When the temperature of the water increases, the resistance \( X \) of the coil will also increase. This is because the resistance of conductors typically increases with temperature. We denote the new resistance as \( X' \), where \( X' > X \).

### Step 4: Write the New Balancing Condition
With the new resistance \( X' \), the new balancing length \( L' \) can be expressed as:
\[ \frac{X'}{R} = \frac{L'}{100 - L'} \]
Since \( X' > X \), the ratio \( \frac{X'}{R} \) will also be greater than the original ratio \( \frac{X}{R} \).

### Step 5: Analyze the Implications of the Increased Resistance
Given that \( \frac{X'}{R} > \frac{X}{R} \), it follows that:
\[ \frac{L'}{100 - L'} > \frac{L}{100 - L} \]
This indicates that the new balancing length \( L' \) must be greater than the original balancing length \( L \).

### Conclusion
Thus, when the temperature of the water is increased, the new balancing length \( L' \) will be greater than the original balancing length \( L \).

### Final Answer
The new balancing length \( L' \) will be greater than \( L \).