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 find the new resistance of the ammeter after adding the shunt resistance, we can use the formula for the equivalent resistance of a galvanometer with a shunt resistor. The formula is given by:

\[ R = \frac{R_g \cdot r}{R_g + r} \]

where:
- \( R_g \) is the resistance of the galvanometer,
- \( r \) is the shunt resistance.

Given:
- \( R_g = 70 \, \Omega \)
- \( r = 0.03 \, \Omega \)

### Step 1: Substitute the values into the formula

We start by substituting the known values into the formula:

\[ R = \frac{70 \cdot 0.03}{70 + 0.03} \]

### Step 2: Calculate the numerator

Now we calculate the numerator:

\[ 70 \cdot 0.03 = 2.1 \]

### Step 3: Calculate the denominator

Next, we calculate the denominator:

\[ 70 + 0.03 = 70.03 \]

### Step 4: Calculate the equivalent resistance

Now we can calculate the equivalent resistance \( R \):

\[ R = \frac{2.1}{70.03} \]

### Step 5: Perform the division

Now, we perform the division:

\[ R \approx 0.02998 \, \Omega \]

### Step 6: Round the result

Finally, we round the result to three significant figures:

\[ R \approx 0.030 \, \Omega \]

### Conclusion

The new resistance of the ammeter after adding the shunt resistance is approximately \( 0.030 \, \Omega \).

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