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.
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $\mathrm{M}^{\mathrm{B}} \mathrm{L}^{\mathrm{O}} \mathrm{T}^{\mathrm{B}} \mathrm{A}^{\mathrm{S}}$, where value of 'Q' and 'R' are
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Note: Assume a full range of motion is possible for the top plate and there is no fringe capacitance. The permittivity of free space is $\epsilon_0 = 8.85 \times 10^{-12}$ F/m and relative permittivity of air ($\epsilon_r$) is 1.
A 60 V DC source with an internal resistance \(R_{int} = 0.5 \, \Omega\) is connected through a switch to a pair of infinitely long rails separated by \(l = 1\) m as shown in the figure. The rails are placed in a constant, uniform magnetic field of flux density \(B = 0.5\) T, directed into the page. A conducting bar placed on these rails is free to move. At the instant of closing the switch, the force induced on the bar is
Match List-I with List-II: List-I