Chapter 13, Problem 95RE

(a)

To determine

The value of $\sin \theta$ with the help of right triangle.

(b)

To determine

The value of $L_2$ from the result obtained in part (a).

(c)

To determine

The value of $\cot \theta$ in terms of s and $L_0-L_1$.

(d)

To determine

The value of $L_1$ from the result obtained in part (c).

(e)

To determine

An expression for $R_1$ along the length AD.

(f)

To determine

An expression for the resistance along the length DC.

(g)

To determine

To write:  An expression for the resistance R as the sum of resistance along the length AD and DC.

(h)

To determine

To replace:  The expression for the resistance R with the values of $L_1\text{ and }{L}_2$ obtained in part (d) and (b), respectively.

(i)

To determine

The derivative of the expression R with respect to $\theta$.

(j)

To determine

To set:  The derivative of the expression R with respect to $\theta$ to zero.

(k)

To determine

To multiply:  The equation obtained in part (j) by $\frac{{\sin }^2\theta }{s}$.

(l)

To determine

The equation obtained in part (k) for $\cos \theta$.

(m)

To determine

To verify:  The solution obtained in part (l) for $\cos \theta$ gives a minimum.

(n)

To determine

The value of $\cos \theta$ and then the value of $\theta$.

(o)

To determine

To find:  The value of $\cos \theta$ and then the value of $\theta$.