In a balanced metre bridge, the segment of wire opposite to a resistance of `70Omega` is 70 cm. The unknown resistance is

Options

A. `30Omega`
B. `60Omega`
C. `90Omega`
D. `15Omega`

Explanation

To solve the problem, we will use the principle of a balanced meter bridge. The relationship between the resistances and the lengths of the segments on the bridge is given by the formula:

\[ \frac{R_1}{R_2} = \frac{L_1}{L_2} \]

where:
- \( R_1 \) is the known resistance (70 Ω),
- \( R_2 \) is the unknown resistance (which we need to find),
- \( L_1 \) is the length of the wire segment opposite to \( R_1 \) (70 cm),
- \( L_2 \) is the length of the wire segment opposite to \( R_2 \).

Since the total length of the meter bridge is 100 cm, we can find \( L_2 \) as follows:

\[ L_2 = 100 \, \text{cm} - L_1 = 100 \, \text{cm} - 70 \, \text{cm} = 30 \, \text{cm} \]

Now we can substitute the known values into the formula:

\[ \frac{70 \, \Omega}{R_2} = \frac{70 \, \text{cm}}{30 \, \text{cm}} \]

Cross-multiplying gives:

\[ 70 \, \Omega \times 30 \, \text{cm} = R_2 \times 70 \, \text{cm} \]

Now, simplifying this equation:

\[ 2100 \, \Omega \cdot \text{cm} = R_2 \times 70 \, \text{cm} \]

Dividing both sides by 70 cm:

\[ R_2 = \frac{2100 \, \Omega \cdot \text{cm}}{70 \, \text{cm}} = 30 \, \Omega \]

Thus, the unknown resistance \( R_2 \) is:

\[ \boxed{30 \, \Omega} \]