A galvanometer of resistance `50Omega` is converted into an ammeter by connecting a low resistance (shunt) of value `1Omega` in parallel to the galvanometer, S. If full - scale deflection current of the galvanometer is 10 mA, then the maximum current that can be measured by the ammeter is -

Options

A. (a)500 mA
B. (b)510 mA
C. (c)610 mA
D. (d)490 mA

Answer

To solve the problem, we need to determine the maximum current that can be measured by the ammeter when a galvanometer is converted into an ammeter using a shunt resistor. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Circuit Configuration
We have a galvanometer with a resistance \( R_g = 50 \, \Omega \) and a full-scale deflection current \( I_g = 10 \, \text{mA} \). A shunt resistor \( R_s = 1 \, \Omega \) is connected in parallel to the galvanometer.

### Step 2: Apply Kirchhoff's Law
According to Kirchhoff's law, the total current \( I \) flowing through the circuit is the sum of the current through the galvanometer \( I_g \) and the current through the shunt \( I_s \):
\[ I = I_g + I_s \]
Where:
- \( I_g = 10 \, \text{mA} = 0.01 \, \text{A} \)
- \( I_s \) is the current through the shunt.

### Step 3: Determine Voltage Across the Galvanometer
The voltage across the galvanometer can be expressed as:
\[ V_g = I_g \cdot R_g \]
Substituting the known values:
\[ V_g = 0.01 \, \text{A} \cdot 50 \, \Omega = 0.5 \, \text{V} \]

### Step 4: Set Voltage Across the Shunt Equal to Voltage Across the Galvanometer
Since the galvanometer and shunt are in parallel, the voltage across the shunt \( V_s \) is equal to the voltage across the galvanometer:
\[ V_s = I_s \cdot R_s \]
Thus, we can set the equations for voltage equal:
\[ I_s \cdot R_s = V_g \]
Substituting the known values:
\[ I_s \cdot 1 \, \Omega = 0.5 \, \text{V} \]
This simplifies to:
\[ I_s = 0.5 \, \text{A} = 500 \, \text{mA} \]

### Step 5: Calculate the Total Current
Now, substituting \( I_s \) back into the equation for total current:
\[ I = I_g + I_s = 10 \, \text{mA} + 500 \, \text{mA} = 510 \, \text{mA} \]

### Conclusion
The maximum current that can be measured by the ammeter is:
\[ \boxed{510 \, \text{mA}} \]