Chapter 4, Problem 102P

(a)

To determine

Prove that the voltage $v=\frac{v_{1}RL+R\left(v_2-v_1\right)x}{RL+2rLx-2r{x}^2}$ for the given circuit.

(b)

To determine

Prove that the voltage v will be minimum when $x=\frac{L}{v_2-v_1}\left[-v_1\pm \sqrt{v_1{v}_2-\frac{R}{2rL}{\left(v_1-v_2\right)}^2}\right]$.

(c)

To determine

Find the value of distance $x$ derived in Part (b).

(d)

To determine

Find the minimum value of voltage v derived in Part (a).