The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. what resistance must be connected to it in order to convert it into an ammeter of range 0-0.5 A ?

Options

A. 0.5 ohm
B. 0.002 ohm
C. 0.02 ohm
D. 0.2 ohm

Answer

To solve the problem of converting a galvanometer into an ammeter, we will follow these steps:

### Step 1: Identify the given values
- Resistance of the galvanometer, \( R_g = 50 \, \Omega \)
- Maximum current through the galvanometer, \( I_g = 0.002 \, A \)
- Maximum current range of the ammeter, \( I = 0.5 \, A \)

### Step 2: Understand the configuration
To convert the galvanometer into an ammeter, we need to connect a shunt resistance \( R_s \) in parallel with the galvanometer. The total current \( I \) will split between the galvanometer and the shunt resistance.

### Step 3: Apply the current relationship
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 resistance \( I_s \):
\[ I = I_g + I_s \]
From this, we can express the current through the shunt resistance as:
\[ I_s = I - I_g \]

### Step 4: Use the voltage drop relationship
Since the galvanometer and the shunt resistance are in parallel, the voltage drop across both is the same. The voltage drop across the galvanometer can be expressed as:
\[ V_g = I_g \cdot R_g \]
The voltage drop across the shunt resistance can be expressed as:
\[ V_s = I_s \cdot R_s \]
Setting these two voltage drops equal gives us:
\[ I_g \cdot R_g = I_s \cdot R_s \]

### Step 5: Substitute for \( I_s \)
Substituting \( I_s \) from step 3 into the voltage drop equation:
\[ I_g \cdot R_g = (I - I_g) \cdot R_s \]

### Step 6: Rearrange to find \( R_s \)
Rearranging the equation to solve for \( R_s \):
\[ R_s = \frac{I_g \cdot R_g}{I - I_g} \]

### Step 7: Substitute the known values
Now, substituting the known values into the equation:
\[ R_s = \frac{0.002 \, A \cdot 50 \, \Omega}{0.5 \, A - 0.002 \, A} \]

### Step 8: Calculate \( R_s \)
Calculating the denominator:
\[ 0.5 \, A - 0.002 \, A = 0.498 \, A \]
Now substituting this back into the equation for \( R_s \):
\[ R_s = \frac{0.002 \cdot 50}{0.498} \approx \frac{0.1}{0.498} \approx 0.2004 \, \Omega \]
Thus, rounding to two decimal places, we find:
\[ R_s \approx 0.2 \, \Omega \]

### Final Answer:
The resistance that must be connected to the galvanometer to convert it into an ammeter of range 0-0.5 A is approximately \( 0.2 \, \Omega \).

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