Question

If a is equal to 1.2 ± 0.1cm, b=2.0 ± 0.2cm, c=1.05±0.05cm, calculate the following with the errors and standard errors

(i) ab/C³

(ii) ABC

(iii) C²a³/b²

Answer 1

1)

Angular frequency $w=\frac{1}{\sqrt{LC}}$

Put value

$$w=\frac{1}{\sqrt{8\times10^{-3}\times12.5\times10^{-6}}}=3162.27rad/sec$$

Impedance at resonance frequency

$Z_{max}=R=175\Omega$

Maximum current

$I=\frac{V}{R}=\frac{25}{175}=0.142A$

$I_L=\frac{V}{X_L}=\frac{25}{25.29}=0.98A$

Potential difference

$V_c=I\times X_L$

$V_c=0.142\times25.29=3.59V$

$$V_R=IR=0.142\times175=24.85V$$

$V_c=0.142\times25.29=3.59V$