Potentiometers are commonly used sensing elements. (i) Derive the equations for VL and V(o/c) and hence show that the error introduced by loading a potentiometer is given by: (Rp (1-) R1 N(x) = V, (Rp RL S 1+ |x (1- ) Show that this is a maximum when x = 3 and hence find an approximation for (ii) the maximum percentage error. Accurately plot (i.e. not a crude hand-sketch) the variation of error with distance along the wiper. (iii) (iv) How can you use this information in the design of your resistive transducer? If the potentiometer has a resistance of 1 k2, determine the size of the load resistor required to produce less than 0.1% measurement error at (v) x = 0.20 (a) (b) x = 0.67