Question

A circuit element consists of a resistor with value 20Ω and inductor with value 10mH connected in series. A voltage of LaTeX: v(t)=20\cos(1000t+45^{\circ})\text{V}v ( t ) = 20 cos ⁡ ( 1000 t + 45 ∘ ) V is applied across the circuit element. What is the apparent power of the circuit element? Answer in units of VA while omitting the unit. Hint: calculate the current first.

Answer 1

8.97 Watt

Step-by-step explanation:

Resistance, R = 20 ohm

Inductance, L = 10 mH

V(t) = 20 Cos (1000 t + 45°)

Compare with the standard equation

V(t) = Vo Cos(ωt + Ф)

Ф = 45°

ω = 1000 rad/s

Vo = 20 V

Inductive reactance, XL = ωL = 1000 x 0.01 = 10 ohm

impedance is Z.

`Z = \sqrt{R^(2)+X_(L)^(2)}`

`Z = \sqrt{20^(2)+10^(2)}`

Z = 22.36 ohm

`V_(rms)=(V_(0))/(√(2))`

`V_(rms)=(20)/(√(2)) = 14.144 V`

`I_(rms)=(V_(rms))/(Z)=(14.144)/(√(22.36))=0.634 A`

Apparent power is given by

P = Vrms x Irms

P = 14.144 x 0.634

P = 8.97 Watt