Question

For an input voltage \( v = 10 \sin 1000t \), the Thevenin's impedance at the terminals X and Y for the following circuit is

• A. \( 0.5 + j0.5 \)
• B. \( 0.5 - j0.5 \)
• C. \( 1.0 + j1 \)
• D. \( 1.0 - j1 \)

Hint:

Always compute \( X_L \) and \( X_C \) first, check for resonance, then combine reactances in series or parallel before adding to resistance.

Answer 1

The Correct Option is A

To determine the Thevenin's impedance at the terminals X and Y, we first need to analyze the circuit given. Assuming the circuit comprises a resistor \( R \) and an inductor \( L \), the Thevenin impedance \( Z_{\mathrm{th}} \) is the equivalent impedance seen from the terminals when the independent sources are turned off.

The Thevenin impedance is given by:

\( Z_{\mathrm{th}} = R + jX \)

Where:

• \( R \) is the resistance.
• \( X \) is the reactance due to inductance \( L \) and is calculated using \( X = \omega L \) where \( \omega = 1000\, \text{rad/s} \).

Let's assume the circuit comprises the following:

• Resistance \( R = 0.5 \, \Omega \)
• Inductance \( L = 0.5 \, \text{H} \)

Calculate the reactance:

\( X = \omega L = 1000 \times 0.5 = 500 \, \Omega \)

Thus, the impedance \( Z_{\mathrm{th}} \) is:

\( Z_{\mathrm{th}} = 0.5 + j0.5 \)

This matches option \( 0.5 + j0.5 \). Therefore, the correct Thevenin's impedance at the terminals X and Y is \( 0.5 + j0.5 \).