Question

Which phasor diagram represents LCR circuit at resonance?

• A. fig.(c)
• B. fig.(a)
• C. fig.(d)
• D. fig.(b)

Hint:

At resonance the inductive and capacitive voltages are equal and opposite, so only the resistor voltage remains, along the current.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
In a series LCR circuit \(V_{R}\) is in phase with the current, \(V_{L}\) leads the current by \(90^{\circ}\) and \(V_{C}\) lags it by \(90^{\circ}\).

Step 2: At resonance
\(X_{L}=X_{C}\), so \(V_{L}=V_{C}\). They are opposite in direction and cancel.

Step 3: Net voltage
The supply voltage equals \(V_{R}\) and is in phase with the current. The phase angle is zero and the power factor is 1.

Step 4: Identify the figure
The diagram showing \(V_{R}\) along the current with equal and opposite \(V_{L}\) and \(V_{C}\) is fig. (d).

Final Answer:
The resonance phasor diagram is fig. (d). \[ \boxed{\text{(C) }\text{fig.(d)}} \]