Question

In the given circuit, the readings of voltmeters $V_{1}$ and $V_{2}$ are 300 V each. The reading of voltmeter $V_{3}$ and ammeter A are respectively

• A. 100 V, 2.0 A
• B. 150 V, 2.2 A
• C. 220 V, 2.0 A
• D. 220 V, 2.2 A

Hint:

When $V_{L} = V_{C}$, the circuit is in resonance! The entire source voltage drops purely across the resistor ($V_{R} = V_{\text{source}}$), and the impedance becomes minimum ($Z = R$).

Answer 1

The Correct Option is D

Step 1: Concept
In a series LCR circuit, the total alternating voltage $V$ is related to the individual voltages across the resistor ($V_{R}$), inductor ($V_{L}$), and capacitor ($V_{C}$) by the formula $V = \sqrt{V_{R}^2 + (V_{L} - V_{C})^2}$.

Step 2: Meaning
Here, $V_{1}$ measures $V_{L}$ and $V_{2}$ measures $V_{C}$. Since $V_{1} = V_{2} = 300\text{ V}$, the circuit is at electrical resonance. Voltmeter $V_{3}$ is connected across the resistor $R$, meaning $V_{3} = V_{R}$.

Step 3: Analysis
Substituting $V_{L} = V_{C}$ into the voltage equation gives $V = \sqrt{V_{R}^2 + 0} = V_{R}$. Given that the supply voltage is $220\text{ V}$, the reading of voltmeter $V_{3}$ must equal the supply voltage, which is $220\text{ V}$. At resonance, the circuit impedance $Z$ equals the resistance $R = 100\ \Omega$. The current measured by ammeter $A$ is $I = \frac{V}{Z} = \frac{220}{100} = 2.2\text{ A}$.

Step 4: Conclusion
The voltmeter reading $V_{3}$ is 220 V and the ammeter reading is 2.2 A.

Final Answer: (D)