In the measurement of RMS value of a voltage in CRO, the peak-... | Technical Ability MCQ | Examoogle

Technical AbilityElectrical Measurements and Instrumentation

In the measurement of RMS value of a voltage in CRO, the peak-to-peak voltage is divided by which of the following values?

Option 1

Option 2

Option 3

Option 4

Correct Answer

⚙️ TE • Technical Concept & PrincipleTechnical AbilityElectrical Measurements and Instrumentation

Option A

Option 1

Quick Summary:

To calculate the Root Mean Square (RMS) value of a sinusoidal signal using a Cathode Ray Oscilloscope (CRO), one must divide the peak-to-peak voltage ( $V_{p-p}$ ) by $2\sqrt{2}$ . The peak-to-peak voltage is twice the peak amplitude ( $V_{p-p} = 2V_m$ ), and the relationship between the peak amplitude and the RMS value is $V_{rms} = \frac{V_m}{\sqrt{2}}$ .

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$V_{p-p} = 2V_m$

$V_{rms} = \frac{V_m}{\sqrt{2}} = \frac{V_{p-p}}{2\sqrt{2}}$

⚙️ Working Principle

The CRO displays the waveform in the time domain, allowing for visual measurement of the peak-to-peak voltage. By dividing $V_{p-p}$ by $2$ , we obtain the peak voltage ( $V_m$ ). Further dividing by $\sqrt{2}$ converts this peak voltage into the effective RMS value, which is the DC equivalent value for power dissipation in a resistive load.

📌 Key Points

▸
The peak-to-peak voltage is measured between the highest and lowest points of the sine wave on the CRT screen.
▸
The factor $2\sqrt{2}$ is equivalent to approximately $2.828$ .
▸
This calculation assumes a pure sinusoidal waveform; non-sinusoidal waveforms have different form factors.

✅ Advantages

▸
Provides a direct visual method for AC signal analysis.
▸
Useful for observing signal characteristics like distortion and frequency alongside amplitude.

❌ Disadvantages / Limitations

▸
Requires manual calculation and visual estimation, which can introduce reading errors.
▸
Less accurate than dedicated digital multimeters for precise RMS measurements.

🛠️ Applications / Uses

▸
Laboratory signal testing.
▸
Educational demonstrations of electrical wave properties.
▸
Troubleshooting of AC electronic circuits.

📄 Additional Information

▸
The option B represents $2\sqrt{2}$ , which is the correct divisor to convert $V_{p-p}$ directly to $V_{rms}$ .
▸
Options A, C, and D are incorrect mathematical conversions for a sinusoidal waveform.

📊 Diagram / Illustration

✅

B is correct — The RMS voltage is calculated by dividing the peak-to-peak voltage by $2\sqrt{2}$ for a sinusoidal signal.

Core Concepts Used

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RMS Voltage Peak-to-Peak Voltage Cathode Ray Oscilloscope Measurement

💡 EXAM TIP

Always remember that $V_{rms} = 0.707 V_m$ and $V_{p-p} = 2 V_m$ . Combining these gives $V_{rms} = \frac{V_{p-p}}{2 \times 1.414} = \frac{V_{p-p}}{2.828}$ .

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