A current i = 10 sin \(\left( 300 t-\frac{3\pi}{8} \right)\) is produced when a voltage V = 30 sin 300 t is applied to a circuit. The estimated value of impedance is : 

concept:

Impedance(Z) is given as:Z=\( \frac{v(t)}{i(t)} \)

v(t)= V_m sin(wt+\( \phi\))

i(t)=I_m sin(wt+\( \theta\))

it is also written as:

Z=\(\frac{V_m∠\phi} {I_m∠\theta}\)

calculation:

v(t) = 30 sin 300 t = 30∠0º

i(t) = 10 sin \(\left( 300 t-\frac{3\pi}{8} \right)\) = 10∠-67.5º

z= \(\frac { 30∠0} {10∠-67.5}\)

z= 3∠ 67.5º

so correct option is 4.