A galvanometer of resistance `70 Omega`, is converted to an ammeter by a shunt resistance `r_(3) = 0.03 Omega`. The value of its resistance will become

Options

A. `0.025 Omega`
B. `0.022Omega`
C. `0.035Omega`
D. `0.030Omega`

Explanation

To solve the problem of finding the equivalent resistance when a galvanometer is converted to an ammeter using a shunt resistance, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Resistance of the galvanometer, \( R_g = 70 \, \Omega \)
- Shunt resistance, \( r_s = 0.03 \, \Omega \)

2. **Understand the Configuration:**
- The galvanometer and the shunt resistance are connected in parallel. The equivalent resistance \( R \) can be calculated using the formula for resistors in parallel:
\[ \frac{1}{R} = \frac{1}{R_g} + \frac{1}{r_s} \]

3. **Substituting the Values:**
- Plugging in the values of \( R_g \) and \( r_s \) into the formula:
\[ \frac{1}{R} = \frac{1}{70} + \frac{1}{0.03} \]

4. **Calculating Each Term:**
- Calculate \( \frac{1}{70} \):
\[ \frac{1}{70} \approx 0.0142857 \]
- Calculate \( \frac{1}{0.03} \):
\[ \frac{1}{0.03} \approx 33.3333 \]

5. **Adding the Terms:**
- Now, add the two fractions:
\[ \frac{1}{R} = 0.0142857 + 33.3333 \approx 33.3476 \]

6. **Finding the Equivalent Resistance:**
- Now, take the reciprocal to find \( R \):
\[ R \approx \frac{1}{33.3476} \approx 0.02998 \, \Omega \]

7. **Rounding the Result:**
- Rounding \( 0.02998 \) gives approximately \( 0.03 \, \Omega \).

### Final Answer:
The equivalent resistance when the galvanometer is converted to an ammeter is approximately \( 0.03 \, \Omega \).

---