Question

The RMS voltage shown in the waveform is

Answer 1

Step 1: Definition and Given data

RMS voltage of AC waveform: The amount of AC power that delivers the same heating effect as DC power is known as the RMS (Root Mean Square) Voltage of an AC Waveform.

$V_{max}=10\mathrm{V}$

The RMS voltage is shown in the waveform below.

Step 2: Formula used

• $\begin{array}{l}{V}_{RMS}=\sqrt{\frac{1}{T}{\int }_0^T(V_{max}{)}^{2}dT}\end{array}$

Where $V_{RMS}$ is the RMS Voltage,$T$ is the time period, and $V_{max}$ is the maximum voltage.

Step 3: Calculations

• By observing the given waveform

$V_{max}=10V$

Now,

$$\begin{gathered} \begin{array}{l}{V}_{RMS}=\sqrt{\frac{1}{T}{\int }_0^T(10{)}^{2}dT}\end{array} \\ \begin{array}{l}{V}_{RMS}=\sqrt{\frac{1}{T}(10{)}^2{\int }_0^{T}dT}\end{array} \\ \begin{array}{l}{V}_{RMS}=\sqrt{\frac{1}{T}(10{)}^2(T-0)}\end{array} \\ {V}_{RMS}=\begin{array}{l}\sqrt{\frac{1}{T}(10{)}^{2}T}\end{array} \\ {V}_{RMS}=\begin{array}{l}\sqrt{(10{)}^2}=10\mathrm{V}\end{array} \\ {V}_{RMS}=10\mathrm{V} \end{gathered}$$

Hence the RMS Voltage from the given figure is $10\mathrm{V}$.