In a meter bridge, two unknown resistances R and S, when connected between the two gaps, gives a null point is 60 cm from one end. What is the ratio of R and S?

Answer

To solve the problem, we will use the principle of the meter bridge, which states that when the bridge is balanced (null point), the ratio of the resistances is equal to the ratio of the lengths of the wire on either side of the null point.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- In a meter bridge, we have a wire of length 100 cm (1 meter).
- When two resistances R and S are connected, a null point is found at a distance of 60 cm from one end.

2. **Identifying Lengths**:
- The distance from one end to the null point is 60 cm.
- Therefore, the remaining length from the null point to the other end is:
\[ 100 \, \text{cm} - 60 \, \text{cm} = 40 \, \text{cm} \]

3. **Applying the Meter Bridge Formula**:
- According to the meter bridge principle:
\[ \frac{R}{S} = \frac{\text{Length on one side}}{\text{Length on the other side}} \]
- Substituting the lengths we found:
\[ \frac{R}{S} = \frac{60 \, \text{cm}}{40 \, \text{cm}} \]

4. **Simplifying the Ratio**:
- Simplifying the ratio:
\[ \frac{R}{S} = \frac{60}{40} = \frac{3}{2} \]

5. **Conclusion**:
- Therefore, the ratio of the resistances R and S is:
\[ R : S = 3 : 2 \]