Chapter 1, Problem 1.8.3E

Explanation of Solution

We have,

The reduction in total dissipated power is 10%

Then,

$\frac{{\text{(S}}_{\text{new}}\text{+}{\text{D}}_{\text{new}}\text{)}}{{\text{(S}}_{\text{old}}\text{+}{\text{D}}_{\text{old}}\text{)}}\text{=}\text{0}\text{.90}$ (1)

${\text{D}}_{\text{new}}\text{=}\text{C}\text{×}{\text{V}}^{\text{2}}{}_{\text{new}}\text{×}\text{F}$ (2)

${\text{S}}_{\text{old}}\text{=}{\text{V}}_{\text{old}}\text{×}\text{I}$ (3)

${\text{S}}_{\text{new}}\text{=}{\text{V}}_{\text{new}}\text{×}\text{I}$ (4)

From the equation (2)

$\Rightarrow {\text{V}}_{\text{new}}\text{=}{\left[\frac{{\text{D}}_{\text{new}}}{\text{C}\text{×}\text{F}}\right]}^{\text{1/2}}$ (5)

From the equation (1)

$\Rightarrow {\text{D}}_{\text{new}}\text{=}\text{0}\text{.90}\text{×}{\text{(S}}_{\text{old}}\text{+}{\text{D}}_{\text{old}}\text{)}\text{-}{\text{S}}_{\text{new}}$ (6)

From the equation (3) and (4)

$\Rightarrow \frac{{\text{S}}_{\text{new}}}{{\text{V}}_{\text{new}}}\text{=}\frac{{\text{S}}_{\text{old}}}{{\text{V}}_{\text{old}}}$

$\Rightarrow {\text{S}}_{\text{new}}\text{=}{\text{V}}_{\text{new}}\text{×}\frac{{\text{S}}_{\text{old}}}{{\text{V}}_{\text{old}}}$ (7)

Substitute, “10” for “S_old” and “1.25” for “V_old” in the equation (7)

${\text{S}}_{\text{new}}\text{=}{\text{V}}_{\text{new}}\text{×}\frac{\text{10}}{\text{1}\text{.25}}$

$\text{S}{}_{\text{new}}\text{=}{\text{V}}_{\text{new}}\text{×}\text{8}$

Substitute, “${\text{V}}_{\text{new}}\text{×}\text{8}$” for “S_new”, “10” for “S_old” and “90” for “D_old” in the equation(6)

$\begin{array}{c}{\text{D}}_{\text{new}}\text{=}\text{0}\text{.90}\text{×}\text{(10}\text{+}\text{90)}\text{-}{\text{(V}}_{\text{new}}\text{×}\text{8)}\\ \text{=}\text{(0}\text{.90}\text{×}\text{100)}\text{-}{\text{(V}}_{\text{new}}\text{×}\text{8)}\\ \text{=}\text{90}\text{-}{\text{(V}}_{\text{new}}\text{×}\text{8)}\end{array}$

Substitute “$\text{90}\text{-}{\text{(V}}_{\text{new}}\text{×}\text{8)}$” for “D_new”, “$\text{3}$