Question

What is the shunt resistance \(S\) needed if the galvanometer current \(I_g\) is \(8\%\) of the total current \(I\)?

• A. \(\frac{2G}{23}\)
• B. \(\frac{8G}{23}\)
• C. \(\frac{23G}{2}\)
• D. \(\frac{G}{23}\)

Hint:

In a galvanometer–shunt combination, use \(I_gG = I_sS\). The shunt carries the majority of the current, protecting the galvanometer from large currents.

Answer 1

The Correct Option is A

Topic - Physics: Current Electricity (Magnetic Effect of Electric Current)
Step 1: Understanding the Question:
We need to calculate the value of the shunt resistance (\(S\)) required to convert a galvanometer of resistance \(G\) into an ammeter such that only \(8%\) of the total current passes through the galvanometer.
Step 2: Key Formula or Approach:
For a galvanometer and shunt in parallel:
\[ I_g G = (I - I_g) S \]
Rearranging for \(S\):
\[ S = \frac{I_g}{I - I_g} G \]
Step 3: Detailed Solution:
Given: \(I_g = 8%\) of \(I = 0.08 I\).
Current through the shunt \(I_s = I - I_g = I - 0.08 I = 0.92 I\).
Using the formula:
\[ S = \frac{0.08 I}{0.92 I} G \]
\[ S = \frac{0.08}{0.92} G \]
\[ S = \frac{8}{92} G \]
Dividing both by 4:
\[ S = \frac{2}{23} G \]
Step 4: Final Answer:
The shunt resistance is \(S = \frac{2G}{23}\).