Chapter 2 Units and Measurement Lecture 9

Our greatest fear should not be of failure but of succeeding at things in life that don’t really matter. – Francis Chan

Example 2.9 The resistance R = V/I where V = (100 ± 5)V and I = (10 ± 0.2)A. Find the percentage error in R.

Example 2.10 Two resistors of resistances R1 = 100±3 ohm and R2 = 200 ± 4 ohm are connected
(a) in series,
(b) in parallel.
Find the equivalent resistance of the
(a) series combination,
(b) parallel combination.
Use for (a) the relation R = R1 + R2 and for (b) \( \frac{1}{R`} = \frac{1}{R_1} + \frac{1}{R_2}\) and \( \frac{\Delta R`}{R`^{2}} = \frac{\Delta R_1}{{R_1}^2} + \frac{\Delta R_2}{{R_2}^2}\)

Example 2.11 Find the relative error in Z, if \(Z = \frac{A^4 B^{\frac{1}{3}}}{C D^{\frac{3}{2}}}\).

Example 2.12 The period of oscillation of a simple pendulum is \( T = 2 \pi \sqrt{\frac{L}{g}}\)
Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g ?