RMS Value

Problem-Solving Strategy for solving the RMS Values

STEP 1. At first, the rms value of voltage is as follows: $V_{rms}=\sqrt{\frac{1}{T}\intop\nolimits_{t_0}^{t_0+T}v^2(t) dt}$

STEP 2. Similarly, the rms value of current is as follows: $I_{rms}=\sqrt{\frac{1}{T}\intop\nolimits_{t_0}^{t_0+T}i^2(t) dt}$

Note: This post is based on Irwin's Basic Engineering Circuit Analysis 11th ed.

If there are any errors in solution, please let me know in the comments

The waveform is periodic with period $T=6s$. The equation for the voltage in the time frame $0\leq t\leq 6s$ is

$\begin{Bmatrix}-4V &(0 \leq t<2s)\\(-2t+8)V &(2s \leq t<4s)\\0V &(4s \leq t<6s)\end{Bmatrix}$

The rms value is

$V_{rms}=\sqrt{\frac{1}{6}[\intop\nolimits_{0}^{2}(-4)^2 dt+\intop\nolimits_{2}^{4}(-2t+8)^2 dt+\intop\nolimits_{4}^{6}(0)^2 dt]}=2.667V$