A galvanometer having a resistance of 8 ohm is shunted by a wire of resistance 2 ohm . If the total current is 1 amp , the part of it passing through the shunt will be

Options

A. `0.2`amp
B. `0.8` amp
C. `0.2` amp
D. `0.5` amp

Answer

To solve the problem step by step, we will use the principles of parallel circuits and Ohm's law.

### Step 1: Understand the Circuit Configuration
We have a galvanometer with a resistance \( G = 8 \, \Omega \) and a shunt resistance \( S = 2 \, \Omega \). The total current flowing through the circuit is \( I = 1 \, \text{A} \).

### Step 2: Apply the Current Division Rule
In a parallel circuit, the total current \( I \) splits between the galvanometer and the shunt. Let \( I_G \) be the current through the galvanometer and \( I_S \) be the current through the shunt. According to the current division rule:
\[ I = I_G + I_S \]
Thus, we can express the current through the shunt as:
\[ I_S = I - I_G \]

### Step 3: Use Ohm's Law for the Galvanometer and Shunt
Since both the galvanometer and the shunt are in parallel, they have the same voltage across them. According to Ohm's law:
\[ V = I_G \cdot G = I_S \cdot S \]
Substituting \( I_S \) from the previous equation:
\[ I_G \cdot G = (I - I_G) \cdot S \]

### Step 4: Substitute Known Values
Substituting the values of \( G \) and \( S \):
\[ I_G \cdot 8 = (1 - I_G) \cdot 2 \]

### Step 5: Solve for \( I_G \)
Expanding the equation:
\[ 8 I_G = 2 - 2 I_G \]
Combining like terms:
\[ 8 I_G + 2 I_G = 2 \]
\[ 10 I_G = 2 \]
\[ I_G = \frac{2}{10} = \frac{1}{5} \, \text{A} \]

### Step 6: Calculate the Current through the Shunt
Now, we can find the current through the shunt \( I_S \):
\[ I_S = I - I_G = 1 - \frac{1}{5} = \frac{4}{5} \, \text{A} \]

### Final Answer
The part of the total current passing through the shunt is:
\[ I_S = \frac{4}{5} \, \text{A} = 0.8 \, \text{A} \]