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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.

Respuesta :

Answer:

8.97 Watt

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.

[tex]Z = \sqrt{R^{2}+X_{L}^{2}}[/tex]

[tex]Z = \sqrt{20^{2}+10^{2}}[/tex]

Z = 22.36 ohm

[tex]V_{rms}=\frac{V_{0}}{\sqrt{2}}[/tex]

[tex]V_{rms}=\frac{20}{\sqrt{2}} = 14.144 V[/tex]

[tex]I_{rms}=\frac{V_{rms}}{Z}=\frac{14.144}{\sqrt{22.36}}=0.634 A[/tex]

Apparent power is given by

P = Vrms x Irms

P = 14.144 x 0.634

P = 8.97 Watt

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