Question:
In Maxwell's capacitance bridge for calculating unknown inductance, the various values at balance are \( R_2 = 300 \, \Omega \), \( R_3 = 700 \, \Omega \), \( R_4 = 1500 \, \Omega \), \( C_4 = 0.8 \, \mu\text{F} \). Calculate \( R_1 \), \( L_1 \), and Q factor, if the frequency is 1100 Hz.
In Maxwell's capacitance bridge for calculating unknown inductance, the various values at balance are \( R_2 = 300 \, \Omega \), \( R_3 = 700 \, \Omega \), \( R_4 = 1500 \, \Omega \), \( C_4 = 0.8 \, \mu\text{F} \). Calculate \( R_1 \), \( L_1 \), and Q factor, if the frequency is 1100 Hz.
Show Hint
In Maxwell's capacitance bridge, the unknown values can be directly calculated using:
\[
R_1 = \frac{R_2 R_3}{R_4}, \quad L_1 = C_4 R_2 R_3
\]
Always remember to convert microfarads to farads. To find the Q factor, use \( Q = \frac{\omega L_1}{R_1} \) with \( \omega = 2\pi f \).
Updated On: Jun 11, 2025
- \( 240 \, \Omega,\ 0.12 \, \text{H},\ 3.14 \)
- \( 140 \, \Omega,\ 0.168 \, \text{H},\ 8.29 \)
- \( 140 \, \Omega,\ 0.12 \, \text{H},\ 5.92 \)
- \( 240 \, \Omega,\ 0.36 \, \text{H},\ 8.29 \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Understanding the Problem:
- Maxwell's capacitance bridge is used to measure unknown inductance (\(L_1\)) and resistance (\(R_1\)).
- At balance, the impedance ratios of the bridge arms are equal.
- The Q factor (Quality Factor) of the coil is calculated using the formula \(Q = \frac{\omega L_1}{R_1}\).
Formulae:
- Balance condition for Maxwell's bridge: \(\frac{R_1}{R_2} = \frac{R_3}{R_4} + j\omega C_4 R_3\).
- Inductance calculation: \(L_1 = R_2 R_3 C_4\).
- Q factor: \(Q = \frac{\omega L_1}{R_1} = \omega C_4 R_4\).
Given Values:
- \(R_2 = 300 \, \Omega\)
- \(R_3 = 700 \, \Omega\)
- \(R_4 = 1500 \, \Omega\)
- \(C_4 = 0.8 \, \mu\text{F} = 0.8 \times 10^{-6} \, \text{F}\)
- Frequency (\(f\)) = 1100 Hz
- Angular frequency (\(\omega\)) = \(2\pi f = 2\pi \times 1100 \, \text{rad/s}\)
Calculating \(R_1\):
From the balance condition:
\(\frac{R_1}{R_2} = \frac{R_3}{R_4}\)
\(R_1 = R_2 \times \frac{R_3}{R_4}\)
\(R_1 = 300 \times \frac{700}{1500} = 140 \, \Omega\)
Calculating \(L_1\):
Using the inductance formula:
\(L_1 = R_2 R_3 C_4\)
\(L_1 = 300 \times 700 \times 0.8 \times 10^{-6}\)
\(L_1 = 168 \times 10^{-3} \, \text{H} = 0.168 \, \text{H}\)
Calculating Q Factor:
Using the Q factor formula:
\(Q = \omega C_4 R_4\)
\(Q = 2\pi \times 1100 \times 0.8 \times 10^{-6} \times 1500\)
\(Q = 2\pi \times 1100 \times 1.2 \times 10^{-3}\)
\(Q = 8.29\)
Final Answer:
\(R_1 = 140 \, \Omega\), \(L_1 = 0.168 \, \text{H}\), \(Q = 8.29\)
Was this answer helpful?
1
0
Top TS PGECET Biomedical Engineering Questions
- The voltage applied to a 212 mH inductor is given by $V(t)=15e^{-5t}$ V. Calculate the current
- The voltage across a capacitor of 0.5F is defined by $V(t)=\begin{cases} 0, & t<0 \\ 2t, & 0<t<2s \\ 4e^{-(t-2)}, & t>2s \end{cases}$. Find $i(t)$
What is the voltage across the inductor at $t=0$? (Circuit diagram provided: A 60V voltage source in series with a switch that closes at $t=0$, a 30 ohm resistor, and a 15H inductor.)
- Which law states that the current flowing into junction must be equal to the current flowing out of it?
- For a voltage source to be neglected, the terminals across the source should be
View More Questions
Top TS PGECET Control Systems Questions
- Systematic errors lead due to a lack of
- Starting position of an object is represented as \( x = 5.1 \pm 0.2 \text{ m} \) and the finishing position as \( y = 6.9 \pm 0.3 \text{ m} \). What will be the displacement and error in displacement?
- A Daniel cell is balanced at 240 cm in length of a potentiometer. Now the cell is short-circuited by a resistance of 0.25 ohm and the balance is obtained at 80 cm. The internal resistance of the Daniel cell is
- In a Q Meter, the values of the tuning capacitor are \( C_3 \) and \( C_4 \) for resonant frequencies \( f \) and \( 2f \), respectively. The value of distributed capacitance is
Top TS PGECET Questions
- If \( P = \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{pmatrix} \) is the modal matrix of \( A = \begin{pmatrix} 1 & 1 & 0 \\ 0 & 2 & 2 \\ 0 & 0 & 3 \end{pmatrix} \) then the sum of all the elements of \( P^{-1}AP \) is
- If the system of equations \( kx + y + z = k - 1 \), \( x + ky + z = k - 1 \), and \( x + y + kz = k - 1 \) has infinite solutions, then \( k \) is
- The value of the integral \( \int_C (2xy - x^2) \, dx + (x^2 + y^2) \, dy \) where \( C \) is the boundary of the region enclosed by \( y = x^2 \) and \( y^2 = x \), described in the positive sense, is
- Let \( f(x) = \log x \). The number \( C \) strictly between \( e^2 \) and \( e^3 \) such that its reciprocal is equal to \( \frac{f(e^3) - f(e^2)}{e^3 - e^2} \) is
- The solution of the differential equation \( (D^2 + 2)y = x^2 \) is
View More Questions