Question

Let Q=(1/R) * sqrt(L/C)

Suppose that L decreases by 2.8%. R decreases by 3.5% and C increases by 5%. Use the small increments method to calculate the percentage in Q. Is the change an increase, a decrease or does Q remain unchanged? Give reasons for your answers.

Answer 1

2,8% from L is 0.028L, so L' equal L-0,028L=0,972L

3,5% from R is 0.028R, so R' equal R-0,035R=0,965R

5% from C is 0.05C, so C' equal C+0,05C=1,05C

$Q'=\frac{1}{R'} \sqrt{\frac{L'}{C'}}$

$\frac{Q'}{Q}= \frac{R}{0,965R} \sqrt{ \frac{0.972L C}{1.05CL}}=\frac{1}{0.965} \sqrt{ \frac{0.972}{1.05}}=0.973$

0.973<1 so Q'<Q, so Q decrease