The resistance of a galvanometer is 90 ohm s. If only 10 percent of the main current may flow through the galvanometer, in which way and of what value, a resistor is to be used

Options

A. `10 Omega` in series
B. `10 Omega` in parallel
C. `810 Omega` in series
D. `810 Omega` in parallel

Answer

To solve the problem, we need to determine the value and configuration of a resistor (shunt resistor) that should be used with a galvanometer so that only 10% of the main current flows through it. Here’s a step-by-step solution:

### Step 1: Understand the Configuration
Since we want only 10% of the main current to flow through the galvanometer, we need to connect a resistor (shunt resistor) in parallel with the galvanometer. In a parallel configuration, the voltage across both components is the same, but the current divides between them.

**Hint:** Remember that in parallel circuits, the voltage remains constant across all components.

### Step 2: Define the Terms
Let:
- \( I \) = total (main) current flowing through the circuit.
- \( I_g \) = current through the galvanometer = 10% of \( I \) = \( \frac{10}{100} I = 0.1 I \).
- \( I_s \) = current through the shunt resistor \( S \) = 90% of \( I \) = \( \frac{90}{100} I = 0.9 I \).

**Hint:** Identify the relationship between the currents in the parallel circuit.

### Step 3: Apply Ohm’s Law
According to Ohm's Law, the voltage across the galvanometer (V) can be expressed as:
\[ V = I_g \times R_g \]
Where \( R_g \) is the resistance of the galvanometer (90 ohms).

Thus,
\[ V = (0.1 I) \times 90 = 9 I \]

**Hint:** Use Ohm's Law to relate voltage, current, and resistance.

### Step 4: Write the Voltage Equation for the Shunt Resistor
The voltage across the shunt resistor \( S \) is also equal to the voltage across the galvanometer:
\[ V = I_s \times S \]
Substituting \( I_s = 0.9 I \):
\[ V = (0.9 I) \times S \]

**Hint:** Set the voltage expressions equal since they are in parallel.

### Step 5: Equate the Two Voltage Expressions
Now we can set the two voltage expressions equal to each other:
\[ 9 I = (0.9 I) \times S \]

### Step 6: Simplify the Equation
Dividing both sides by \( I \) (assuming \( I \neq 0 \)):
\[ 9 = 0.9 S \]

### Step 7: Solve for the Shunt Resistance \( S \)
Now, solve for \( S \):
\[ S = \frac{9}{0.9} = 10 \, \text{ohms} \]

**Hint:** Isolate the variable to find the value of the shunt resistor.

### Step 8: Conclusion
The value of the shunt resistor \( S \) is 10 ohms, and it should be connected in parallel with the galvanometer.

**Final Answer:** A 10-ohm resistor should be connected in parallel with the galvanometer.