In meter bridge , the balancing length from left is found to be 20 cm when standard connected of `1 Omega` is in right gap . The value of unknown resistance is

Options

A. `0.25 Omega`
B. `0.4 Omega`
C. `0.5 Omega`
D. `4 Omega`

Answer

To find the unknown resistance using the meter bridge method, we can follow these steps:

### Step 1: Understand the Meter Bridge Principle
The meter bridge is based on the principle of Wheatstone bridge. When the bridge is balanced, the ratio of the resistances is equal to the ratio of the lengths on the bridge wire.

### Step 2: Write the Formula
The formula for the meter bridge is given by:
\[ \frac{S}{R} = \frac{L}{100 - L} \]
where:
- \( S \) = unknown resistance
- \( R \) = known resistance (1 ohm in this case)
- \( L \) = balancing length from the left (20 cm in this case)

### Step 3: Substitute the Known Values
We know:
- \( R = 1 \, \Omega \)
- \( L = 20 \, \text{cm} \)

Substituting these values into the formula gives:
\[ \frac{S}{1} = \frac{20}{100 - 20} \]

### Step 4: Simplify the Equation
Now simplify the right side:
\[ \frac{S}{1} = \frac{20}{80} \]

### Step 5: Calculate the Unknown Resistance
Now calculate \( S \):
\[ S = \frac{20}{80} = \frac{1}{4} = 0.25 \, \Omega \]

### Final Answer
The value of the unknown resistance \( S \) is \( 0.25 \, \Omega \).

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