A galvanometer has resistance `36Omega` if a shunt of `4Omega` is added with this, then fraction of current that passes through galvanometer is:

Explanation

To solve the problem of finding the fraction of current that passes through the galvanometer when a shunt resistor is added, we can follow these steps:

### Step 1: Identify the given values
- Resistance of the galvanometer, \( R_g = 36 \, \Omega \)
- Resistance of the shunt, \( R_{sh} = 4 \, \Omega \)

### Step 2: Calculate the total resistance in parallel
When a shunt is connected in parallel with the galvanometer, the total resistance \( R_t \) can be calculated using the formula for resistors in parallel:
\[ \frac{1}{R_t} = \frac{1}{R_g} + \frac{1}{R_{sh}} \]

Substituting the values:
\[ \frac{1}{R_t} = \frac{1}{36} + \frac{1}{4} \]

### Step 3: Find a common denominator and simplify
To add the fractions, find a common denominator:
\[ \frac{1}{R_t} = \frac{1}{36} + \frac{9}{36} = \frac{10}{36} = \frac{5}{18} \]

### Step 4: Calculate the total resistance \( R_t \)
Now, take the reciprocal to find \( R_t \):
\[ R_t = \frac{18}{5} \, \Omega \]

### Step 5: Determine the current through the galvanometer
Let \( I \) be the total current entering the parallel combination of the galvanometer and the shunt. The current through the galvanometer \( I_g \) can be calculated using the current division rule:
\[ I_g = I \cdot \frac{R_{sh}}{R_g + R_{sh}} \]

Substituting the values:
\[ I_g = I \cdot \frac{4}{36 + 4} = I \cdot \frac{4}{40} = I \cdot \frac{1}{10} \]

### Step 6: Calculate the fraction of the current through the galvanometer
The fraction of the total current that passes through the galvanometer is given by:
\[ \text{Fraction} = \frac{I_g}{I} = \frac{I \cdot \frac{1}{10}}{I} = \frac{1}{10} \]

### Final Answer
The fraction of the current that passes through the galvanometer is:
\[ \frac{1}{10} \]

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