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. `0.2A`
B. `0.8A`
C. `0.25A`
D. `0.5A`

Answer

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

### Step 1: Identify the given values
- Resistance of the galvanometer (G) = 8 ohms
- Resistance of the shunt (Rs) = 2 ohms
- Total current (I) = 1 ampere

### Step 2: Calculate the equivalent resistance (R) of the parallel circuit
The formula for the equivalent resistance of two resistors in parallel is given by:
\[ \frac{1}{R} = \frac{1}{G} + \frac{1}{Rs} \]
Substituting the values:
\[ \frac{1}{R} = \frac{1}{8} + \frac{1}{2} \]
To calculate this, we find a common denominator:
\[ \frac{1}{R} = \frac{1}{8} + \frac{4}{8} = \frac{5}{8} \]
Now, taking the reciprocal to find R:
\[ R = \frac{8}{5} = 1.6 \text{ ohms} \]

### Step 3: Calculate the total voltage (V) in the circuit
Using Ohm's law, \( V = I \times R \):
\[ V = 1 \text{ A} \times 1.6 \text{ ohms} = 1.6 \text{ volts} \]

### Step 4: Calculate the current through the shunt (I2)
Since the galvanometer and the shunt are in parallel, the voltage across them is the same. We can use Ohm's law again:
\[ V = I2 \times Rs \]
Rearranging gives:
\[ I2 = \frac{V}{Rs} \]
Substituting the known values:
\[ I2 = \frac{1.6 \text{ volts}}{2 \text{ ohms}} = 0.8 \text{ amperes} \]

### Final Answer
The part of the total current passing through the shunt is **0.8 amperes**.

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