An ammeter whose resistance is `180 Omega` gives full scale deflection when current is 2mA. The shunt required to convert it into an ammeter reading 20 mA (in ohms) is

Options

A. 18
B. 20
C. 0.1
D. 10

Answer

To find the resistance of the shunt required to convert the ammeter to read a higher current, we can use the following steps:

### Step 1: Understand the given values
- Resistance of the ammeter, \( R_g = 180 \, \Omega \)
- Full scale deflection current of the ammeter, \( I_g = 2 \, \text{mA} = 0.002 \, \text{A} \)
- Desired maximum current reading, \( I = 20 \, \text{mA} = 0.020 \, \text{A} \)

### Step 2: Calculate the current through the shunt
The current through the shunt, \( I_s \), can be calculated using the formula:
\[ I_s = I - I_g \]
Substituting the known values:
\[ I_s = 0.020 \, \text{A} - 0.002 \, \text{A} = 0.018 \, \text{A} \]

### Step 3: Use the formula for shunt resistance
The relationship between the currents and resistances in the circuit is given by:
\[ \frac{R_g}{R_s} = \frac{I_g}{I_s} \]
Where \( R_s \) is the resistance of the shunt. Rearranging the formula gives:
\[ R_s = R_g \cdot \frac{I_s}{I_g} \]

### Step 4: Substitute the values into the formula
Substituting the known values into the equation:
\[ R_s = 180 \, \Omega \cdot \frac{0.018 \, \text{A}}{0.002 \, \text{A}} \]

### Step 5: Calculate the shunt resistance
Calculating the fraction:
\[ \frac{0.018}{0.002} = 9 \]
Now substituting this back into the equation:
\[ R_s = 180 \, \Omega \cdot 9 = 1620 \, \Omega \]

### Final Answer
The resistance of the shunt required is \( R_s = 1620 \, \Omega \).

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