An ammeter is to be constructed which can read currents up to 2.0 A. Iſ the coil has a resistance of `25Omega` and takes 1 mA for full-scale deflection, what should be the resistance of the shunt used?

Answer

To solve the problem of determining the resistance of the shunt used in an ammeter, we can follow these steps:

### Step 1: Understand the Circuit Configuration
The ammeter consists of a coil (which has a resistance of 25Ω) and a shunt resistor (which we need to find). The coil can handle a maximum current of 1 mA for full-scale deflection.

### Step 2: Identify the Total Current
The ammeter is designed to read currents up to 2 A. Therefore, the total current (I_total) that will pass through the circuit is:
\[ I_{\text{total}} = 2 \, \text{A} \]

### Step 3: Determine the Current through the Coil
Since the coil can only handle 1 mA, the current through the coil (I_coil) is:
\[ I_{\text{coil}} = 1 \, \text{mA} = 0.001 \, \text{A} \]

### Step 4: Calculate the Current through the Shunt
Using Kirchhoff's Current Law (KCL), the current through the shunt (I_shunt) can be calculated as:
\[ I_{\text{shunt}} = I_{\text{total}} - I_{\text{coil}} \]
\[ I_{\text{shunt}} = 2 \, \text{A} - 0.001 \, \text{A} = 1.999 \, \text{A} \]

### Step 5: Apply Ohm's Law to Find the Voltage across the Coil
The voltage across the coil (V_coil) can be calculated using Ohm's Law:
\[ V_{\text{coil}} = I_{\text{coil}} \times R_{\text{coil}} \]
\[ V_{\text{coil}} = 0.001 \, \text{A} \times 25 \, \Omega = 0.025 \, \text{V} \]

### Step 6: Set Up the Equation for the Shunt Resistor
Since the shunt and the coil are in parallel, the voltage across the shunt (V_shunt) is the same as the voltage across the coil:
\[ V_{\text{shunt}} = V_{\text{coil}} \]
Using Ohm's Law for the shunt:
\[ V_{\text{shunt}} = I_{\text{shunt}} \times R_{\text{shunt}} \]
Substituting the known values:
\[ 0.025 \, \text{V} = 1.999 \, \text{A} \times R_{\text{shunt}} \]

### Step 7: Solve for the Shunt Resistance
Rearranging the equation gives:
\[ R_{\text{shunt}} = \frac{0.025 \, \text{V}}{1.999 \, \text{A}} \]
Calculating this gives:
\[ R_{\text{shunt}} \approx \frac{0.025}{2} = 0.0125 \, \Omega \]

### Final Answer
The resistance of the shunt used should be approximately:
\[ R_{\text{shunt}} \approx 0.0125 \, \Omega \]