For a R-L-C series circuit connected to the input signal 4Vp-p... | Technical MCQ | Examoogle

TechnicalElectrical Engineering

For a R-L-C series circuit connected to the input signal 4Vp-p,1KHz periodic sinusoidal ac signal and the voltage drop across the resistor R measured with the help of CRO displays a sine wave occupying 2 units total height and volts /div knob at 1V,then the RMS current for the circuit is approximately ______________ if R=10Ω.

414A

0.071A

0.71 A

0.14 A

Correct Answer

⚙️ TE • Technical Concept & PrincipleTechnicalElectrical Engineering

Option C

0.71 A

Quick Summary:

To find the RMS current, we first determine the peak-to-peak voltage across the resistor using the CRO settings. The total height of 2 units with a scale of 1V/div gives a peak-to-peak voltage of 2V, implying a peak voltage ( $V_p$ ) of 1V. Using Ohm's Law and the conversion factor for a sinusoidal wave, the RMS current is calculated as $I_{rms} = \frac{V_p}{\sqrt{2} \times R} = \frac{1}{1.414 \times 10} \approx 0.0707A$ .

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of a swing oscillating; the peak-to-peak distance is the total width of the swing's path, while the amplitude is just the distance from the center rest position to one side.

🧠 Memory Mnemonic / Shortcut Aid

Remember 'PI-RMS': Peak to Peak divide by 2 gives Peak, then Peak divided by root 2 gives RMS current.

🔢 Key Formulas

$V_p = \frac{V_{p-p}}{2}$ — Relationship between peak-to-peak and peak voltage

$I_{rms} = \frac{I_p}{\sqrt{2}} = \frac{V_p}{R \times \sqrt{2}}$ — Conversion to RMS current for sinusoidal waveforms

⚙️ Working Principle

A Cathode Ray Oscilloscope (CRO) displays voltage over time. The peak-to-peak voltage ( $V_{p-p}$ ) represents the total vertical displacement. Since $V_p = \frac{V_{p-p}}{2}$ , the amplitude is 1V. By applying Ohm's Law ( $I = \frac{V}{R}$ ), we find the peak current ( $I_p$ ). The RMS value of a sine wave is derived by dividing the peak value by $\sqrt{2}$ (approximately 1.414).

📌 Key Points

▸
The CRO measures peak-to-peak voltage, which must be halved to find the amplitude ( $V_p$ ).
▸
RMS (Root Mean Square) is the effective value of AC current that provides the same heating effect as DC current.
▸
For sinusoidal signals, the form factor is $\frac{\pi}{2\sqrt{2}} \approx 1.11$ .

✅ Advantages

▸
CRO provides a visual representation of waveform parameters like frequency and amplitude.

❌ Disadvantages / Limitations

▸
RMS calculations using visual CRO data are prone to rounding errors if the scale factor is misinterpreted.

🛠️ Applications / Uses

▸
Audio signal analysis in electronics
▸
Power quality monitoring in power systems

📄 Additional Information

▸
The calculated value $I_{rms} \approx 0.0707 A$ , which rounds to $0.071 A$ .
▸
Option A is incorrect because it confuses the peak current with RMS.
▸
Option D is incorrect because it forgets to divide by $\sqrt{2}$ correctly in the final step.

📊 Diagram / Illustration

✅

C is correct — The RMS current is approximately 0.071A, derived by calculating peak voltage from CRO data and dividing by $\sqrt{2}$ and resistance.

Core Concepts Used

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AC Circuit Analysis CRO Measurements RMS Value Calculation

💡 EXAM TIP

In competitive exams, always verify if the CRO is set to peak-to-peak or RMS mode; if not specified, it always displays peak-to-peak values.

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