In an a.c. circuit, the instantaneous values of e.m.f. and current are $E = 200 s i n (314 t) V a n d I = s i n (314 t + \frac{π}{3}) A$ . The average power consumed (in $W$ ) is

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Solution

$P_{a v} = E_{r m s} I_{r m s} c o s ϕ$
From given equation
$E_{r m s} = \frac{200}{\sqrt{2}}$
$I_{r m s} = \frac{1}{\sqrt{2}}$
$ϕ = 60^{\circ}$

$\Rightarrow P_{a v} = \frac{200 \times 1}{2} \times c o s \frac{π}{3}$

$\Rightarrow \frac{200 \times \frac{1}{2}}{2} = 50 W$

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In an a.c. circuit, the instantaneous values of e.m.f. and current are E=200 sin (314 t) V and I=sin(314 t+π3) A. The average power consumed (in W) is

Pav=ErmsIrmscosϕ From given equation Erms=200√2 Irms=1√2 ϕ=60∘ ⇒Pav=200×12×cosπ3 ⇒200×122=50 W

In an a.c. circuit, the instantaneous values of e.m.f. and current are $E = 200 s i n (314 t) V a n d I = s i n (314 t + \frac{π}{3}) A$ . The average power consumed (in $W$ ) is

$P_{a v} = E_{r m s} I_{r m s} c o s ϕ$
From given equation
$E_{r m s} = \frac{200}{\sqrt{2}}$
$I_{r m s} = \frac{1}{\sqrt{2}}$
$ϕ = 60^{\circ}$

$\Rightarrow P_{a v} = \frac{200 \times 1}{2} \times c o s \frac{π}{3}$

$\Rightarrow \frac{200 \times \frac{1}{2}}{2} = 50 W$