The reading of the ammeter and voltmeter are ( Both the instruments are ac meters and measures rms value) -

Options

A. 2A , 110 V
B. 2 A, 0 V
C. 2V , 55 V
D. 1 A, 0 V

Answer

To solve the problem, we need to analyze the given AC circuit and determine the readings of the ammeter and voltmeter. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Circuit Components
We have an AC circuit with:
- Resistance (R) = 55 ohms
- Inductive reactance (XL) = 2 ohms
- Capacitive reactance (XC) = 2 ohms

### Step 2: Determine the Condition of the Circuit
Since XL = XC, the circuit is in resonance. In a resonant LCR circuit, the total impedance (Z) is equal to the resistance (R) because the inductive and capacitive reactances cancel each other out.

### Step 3: Calculate the Impedance (Z)
Using the formula for impedance in a series LCR circuit:
\[ Z = \sqrt{R^2 + (XL - XC)^2} \]
Since XL = XC, the equation simplifies to:
\[ Z = \sqrt{R^2} = R \]
Thus,
\[ Z = 55 \, \text{ohms} \]

### Step 4: Calculate the RMS Current (Irms)
The RMS voltage (Vrms) provided is 110 volts. The relationship between voltage, current, and impedance is given by Ohm's law:
\[ Irms = \frac{Vrms}{Z} \]
Substituting the known values:
\[ Irms = \frac{110 \, \text{V}}{55 \, \text{ohms}} = 2 \, \text{A} \]

### Step 5: Determine the Voltmeter Reading
In a resonant circuit, the voltmeter measures the voltage across the inductor and capacitor, which cancel each other out, resulting in:
\[ V_{L} = V_{C} \]
Thus, the voltmeter reading is:
\[ V_{rms} = 0 \, \text{V} \]

### Final Readings
- **Ammeter Reading (Irms)**: 2 A
- **Voltmeter Reading (Vrms)**: 0 V

### Summary of Results
The ammeter reads 2 A, and the voltmeter reads 0 V.

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