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)

Hint:

For a balanced bridge, the ratio of resistances is equal to the ratio of the inductance to the product of resistance and capacitance.

Answer 1

Correct Answer: 14.4

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 \( 14.40 \, \text{mH} \).