Question

In an LCR series circuit, at resonance,

• A. the voltage across R is zero.
• B. the voltage across R equals to applied voltage.
• C. the voltage across C is zero.
• D. the voltage across C equals applied voltage.

Hint:

At resonance the reactances cancel, the impedance equals R, and the whole applied voltage appears across the resistor.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In a series LCR circuit the impedance is \(Z=\sqrt{R^{2}+(X_{L}-X_{C})^{2}}\).

Step 2: Calculation
At resonance \(X_{L}=X_{C}\), so \(Z=R\) and the current is maximum, \(I=\frac{V}{R}\). The voltage across \(R\) is \(IR=V\).

Step 3: Compare the options
The voltages across L and C are equal in size but opposite in phase, so they cancel. Each of them is not zero. So the voltage across R equals the applied voltage.

Final Answer:
At resonance the voltage across R equals the applied voltage. \[ \boxed{\text{(B) }\text{the voltage across R equals the applied voltage}} \]