Given:
- Resistance of galvanometer: \( R_g = 100 \, \Omega \)
- Series resistance: \( R_s = 400 \, \Omega \)
- Voltage measured: \( V = 10 \, \text{V} \)
Step 1: Calculating the Current through the Galvanometer
The current through the galvanometer, \( i_g \), is given by:
\[ i_g = \frac{V}{R_g + R_s} = \frac{10}{400 + 100} = \frac{10}{500} = 20 \times 10^{-3} \, \text{A}. \]
Step 2: Converting the Galvanometer to an Ammeter
To convert the galvanometer into an ammeter that can read up to 10 A, we need to connect a shunt resistance \( S \) in parallel with the galvanometer. The shunt resistance is given by:
\[ i_g R_g = (I - i_g) S, \]
where \( I = 10 \, \text{A} \) is the total current.
Rearranging for \( S \):
\[ S = \frac{i_g R_g}{I - i_g} = \frac{20 \times 10^{-3} \times 100}{10 - 20 \times 10^{-3}}. \]
Simplifying:
\[ S = \frac{2}{9.98} \approx 0.2 \, \Omega. \]
Step 3: Expressing \( S \) in the Required Form
Given that \( S = x \times 10^{-2} \, \Omega \), we have:
\[ x = 20. \]
Therefore, the value of \( x \) is 20.
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32