Question:
The bridge shown is balanced when \( R_1 = 100 \, \Omega \), \( R_2 = 210 \, \Omega \), \( C_2 = 2.9 \, \mu\text{F} \), and \( R_4 = 50 \, \Omega \). The 2 kHz sine-wave generator supplies a voltage of 10 V\(_\text{p-p}\). The value of \( L_3 \) (in millihenry) is _________ (round off to two decimal places)
The bridge shown is balanced when \( R_1 = 100 \, \Omega \), \( R_2 = 210 \, \Omega \), \( C_2 = 2.9 \, \mu\text{F} \), and \( R_4 = 50 \, \Omega \). The 2 kHz sine-wave generator supplies a voltage of 10 V\(_\text{p-p}\). The value of \( L_3 \) (in millihenry) is _________ (round off to two decimal places)
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For a balanced bridge, the ratio of resistances is equal to the ratio of the inductance to the product of resistance and capacitance.
Updated On: Nov 25, 2025
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Correct Answer: 14.4
Solution and Explanation
For a balanced bridge, the relationship between the components is given by the following equation:
\[
\frac{R_1}{R_2} = \frac{L_3}{R_4 C_2}.
\]
Substitute the given values:
\[
\frac{100}{210} = \frac{L_3}{50 \times 2.9 \times 10^{-6}}.
\]
Solving for \( L_3 \):
\[
L_3 = \frac{100}{210} \times 50 \times 2.9 \times 10^{-6} = 14.4 \times 10^{-3} \, \text{H} = 14.40 \, \text{mH}.
\]
Thus, the value of \( L_3 \) is \( 14.40 \, \text{mH} \).
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