Chapter 16, Problem 2PP

To determine

The missing values.

Answer to Problem 2PP

Sr No	Peak	RMS	Full Wave Rectified Average
1	12.7	8.98	8.09
2	76.08	53.8	48.42
3	257.30	182.26	164.2
4	1235	873.28	786.70
5	339.41	240	216
6	26.01	18.43	16.6
7	339.7	240.2	216.39
8	17.82	12.6	11.34
9	14.10	9.99	9
10	123.7	87.46	78.79
11	105.78	74.8	67.32
12	169.24	119.88	108

Explanation of Solution

Description:

For (1) :

• To convert from Peak to RMS, multiply peak by $\frac{1}{\sqrt{\text{2}}}$

  $\begin{array}{l}{E}_{rms}=E_{\max }\times \frac{1}{\sqrt{\text{2}}}\\ =\frac{12.7}{\sqrt{\text{2}}}\\ =8.98\text{ V}\end{array}$

• To convert from Peak to Full wave rectified average, multiply peak by $0.637$

  $\begin{array}{l}{E}_{avg}=E_{\max }\times 0.637\\ =12.7\times 0.637\\ =8.09\text{ V}\end{array}$

For (2) :

• To convert from RMS to Peak, divideRMS by $\frac{1}{\sqrt{\text{2}}}$

  $\begin{array}{l}{E}_{\max }=\frac{E_{rms}}{\frac{1}{\sqrt{\text{2}}}}\\ =E_{rms}\sqrt{2}\\ =53.8\sqrt{2}\\ =76.08\text{ V}\end{array}$

• To convert from RMS to Full wave rectified average, multiply RMS by $0.9$

  $\begin{array}{l}{E}_{avg}=E_{rms}\times 0.9\\ =53.8\times 0.9\\ =48.42\text{ V}\end{array}$

For (3) :

• To convert from Average to Peak, multiply Average by 1.567

  $\begin{array}{l}{E}_{\max }=E_{avg}\times 1.567\\ =164.2\times 1.567\\ =257.30\text{ V}\end{array}$

• To convert from Average to RMS, multiply Average by 1.11

  $\begin{array}{l}{E}_{rms}=E_{avg}\times 1.11\\ =164.2\times 1.11\\ =182.26\text{ V}\end{array}$

For (4) :

• To convert from Peak to RMS, multiply peak by $\frac{1}{\sqrt{\text{2}}}$

  $\begin{array}{l}{E}_{rms}=E_{\max }\times \frac{1}{\sqrt{\text{2}}}\\ =\frac{1235}{\sqrt{\text{2}}}\\ =873.28\text{ V}\end{array}$

• To convert from Peak to Full wave rectified average, multiply peak by $0.637$

  $\begin{array}{l}{E}_{avg}=E_{\max }\times 0.637\\ =1235\times 0.637\\ =786.70\text{ V}\end{array}$

For (5) :

• To convert from RMS to Peak, divideRMS by $\frac{1}{\sqrt{\text{2}}}$

  $\begin{array}{l}{E}_{\max }=\frac{E_{rms}}{\frac{1}{\sqrt{\text{2}}}}\\ =E_{rms}\sqrt{2}\\ =240\sqrt{2}\\ =339.41\text{ V}\end{array}$

• To convert from RMS to Full wave rectified average, multiply RMS by $0.9$

  $\begin{array}{l}{E}_{avg}=E_{rms}\times 0.9\\ =240\times 0.9\\ =216\text{ V}\end{array}$

For (6) :

• To convert from Average to Peak, multiply Average by 16.6

  $\begin{array}{l}{E}_{\max }=E_{avg}\times 1.567\\ =16.6\times 1.567\\ =26.01\text{ V}\end{array}$

• To convert from Average to RMS, multiply Average by 1.11

  $\begin{array}{l}{E}_{rms}=E_{avg}\times 1.11\\ =166.6\times 1.11\\ =18.43\text{ V}\end{array}$

For (7) :

• To convert from Peak to RMS, multiply peak by $\frac{1}{\sqrt{\text{2}}}$

  $\begin{array}{l}{E}_{rms}=E_{\max }\times \frac{1}{\sqrt{\text{2}}}\\ =\frac{339.7}{\sqrt{\text{2}}}\\ =240.2\text{ V}\end{array}$

• To convert from Peak to Full wave rectified average, multiply peak by $0.637$

  $\begin{array}{l}{E}_{avg}=E_{\max }\times 0.637\\ =339.7\times 0.637\\ =216.39\text{ V}\end{array}$

For (8) :

• To convert from RMS to Peak, divideRMS by $\frac{1}{\sqrt{\text{2}}}$

  $\begin{array}{l}{E}_{\max }=\frac{E_{rms}}{\frac{1}{\sqrt{\text{2}}}}\\ =E_{rms}\sqrt{2}\\ =12.6\sqrt{2}\\ =17.82\text{ V}\end{array}$

• To convert from RMS to Full wave rectified average, multiply RMS by $0.9$

  $\begin{array}{l}{E}_{avg}=E_{rms}\times 0.9\\ =12.6\times 0.9\\ =11.34\text{ V}\end{array}$

For (9) :

• To convert from Average to Peak, multiply Average by 1.567

  $\begin{array}{l}{E}_{\max }=E_{avg}\times 1.567\\ =9\times 1.567\\ =14.10\text{ V}\end{array}$

• To convert from Average to RMS, multiply Average by 1.11

  $\begin{array}{l}{E}_{rms}=E_{avg}\times 1.11\\ =9\times 1.11\\ =9.99\text{ V}\end{array}$

For (10) :

• To convert from Peak to RMS, multiply peak by $\frac{1}{\sqrt{\text{2}}}$

  $\begin{array}{l}{E}_{rms}=E_{\max }\times \frac{1}{\sqrt{\text{2}}}\\ =\frac{123.7}{\sqrt{\text{2}}}\\ =87.46\text{ V}\end{array}$

• To convert from Peak to Full wave rectified average, multiply peak by $0.637$

  $\begin{array}{l}{E}_{avg}=E_{\max }\times 0.637\\ =12.7\times 0.637\\ =78.79\text{ V}\end{array}$

For (11) :

• To convert from RMS to Peak, divideRMS by $\frac{1}{\sqrt{\text{2}}}$

  $\begin{array}{l}{E}_{\max }=\frac{E_{rms}}{\frac{1}{\sqrt{\text{2}}}}\\ =E_{rms}\sqrt{2}\\ =74.8\sqrt{2}\\ =105.78\text{ V}\end{array}$

• To convert from RMS to Full wave rectified average, multiply RMS by $0.9$

  $\begin{array}{l}{E}_{avg}=E_{rms}\times 0.9\\ =74.8\times 0.9\\ =67.32\text{ V}\end{array}$

For (12) :

• To convert from Average to Peak, multiply Average by 1.567

  $\begin{array}{l}{E}_{\max }=E_{avg}\times 1.567\\ =108\times 1.567\\ =169.24\text{ V}\end{array}$

• To convert from Average to RMS, multiply Average by 1.11

  $\begin{array}{l}{E}_{rms}=E_{avg}\times 1.11\\ =108\times 1.11\\ =119.88\text{ V}\end{array}$