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

# Lecture 9 Units and Measurement

**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 R_{1} = 100±3 ohm and R_{2} = 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 = R_{1} + R_{2} 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 ?