For the balanced Owen-bridge circuit shown in the figure, the values of $L_x$ and $R_x$ are:
Show Hint
- $L_x = \frac{R_2 R_3}{C_3}, R_x = \frac{R_2 C_1}{C_3}$
- $L_x = R_2 R_3 C_1, R_x = \frac{R_2 C_1}{C_3}$
- $L_x = R_2 R_3 C_1, R_x = \frac{R_2 C_3}{C_1}$
- $L_x = \frac{R_2 R_3}{C_3}, R_x = R_2 C_1 C_3$
The Correct Option is B
Solution and Explanation
For a balanced bridge, the following relationships hold:
\[ \frac{R_2}{R_1} = \frac{C_1}{C_3} = \frac{L_x}{L_1} \]
To derive the expressions for $L_x$ and $R_x$:
- The inductance $L_x$ is determined by the ratio of the resistances and capacitances in the bridge: \[ L_x = R_2 R_3 C_1 \]
- The resistance $R_x$ is determined by the ratio of the capacitances and resistances: \[ R_x = \frac{R_2 C_1}{C_3} \]
Thus, the correct answer is option (B):
\[ L_x = R_2 R_3 C_1, \quad R_x = \frac{R_2 C_1}{C_3} \]
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