Question 477: AC fundamentals

Question

The instantaneous values of alternating current and voltage in a circuit are given as 
$$i = {1 \over {\sqrt 2 }}$$ sin (100 $$\pi $$t) ampere
$$e = {1 \over {\sqrt 2 }}\sin \left( {100\pi t + {\pi  \over 3}} \right)$$ Volt
The average power in watts consumed in the circuit is

Accepted Answer

i
rms
= $${{{i_0}} \over {\sqrt 2 }} = {{{1 \over {\sqrt 2 }}} \over {\sqrt 2 }} = {1 \over 2}$$ A
e
rms
= $${{{e_0}} \over {\sqrt 2 }} = {{{1 \over {\sqrt 2 }}} \over {\sqrt 2 }} = {1 \over 2}$$ V
Average power consumed in the circuit,
P = i
rms
e
rms
cos$$\phi $$
= $$\left( {{1 \over 2}} \right)\left( {{1 \over 2}} \right)\cos {\pi  \over 3}$$ = $${1 \over 8}$$ W

Answer

$${1 \over 4}$$

Answer

$${{\sqrt 3 } \over 4}$$

Answer

$${1 \over 2}$$

Answer

$${1 \over 8}$$

AC fundamentals

The instantaneous values of alternating current and voltage in a circuit are given as $i = {1 \over {\sqrt 2 }} sin (100 \pi t) ampere e = {1 \over {\sqrt 2 }}\sin \left( {100\pi t + {\pi \over 3}} \right)$ Volt The average power in watts consumed in the circuit is

Choose the correct answer: