Question 226: AC fundamentals

Question

As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is $${{\sqrt a } \over \pi }$$ A. The value of $$a$$ is ___________.

Accepted Answer

$${I_{rms}} = {{{V_{rms}}} \over z}$$
$$z = {X_2} = {\omega _2}$$
$$ = 2\pi  	imes 50 	imes {{200} \over {1000}}$$
$$ = 20\,\pi $$
$$	herefore$$ $${I_{rms}} = {{220} \over {20\pi }} = {{11} \over \pi }$$
$$	herefore$$ $${I_{peak}} = \sqrt 2  	imes {{11} \over \pi }$$
$$ = {{\sqrt {2 	imes 121} } \over \pi }$$
$$ = {{\sqrt {242} } \over \pi }$$

AC fundamentals

As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is ${{\sqrt a } \over \pi } A. The value of a$ is ___________.

Integer / Numeric Answer Type