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(10

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.

in progress 0
RobertKer 5 years 2021-08-02T10:52:35+00:00 1 Answers 26 views 0

Answers ( )

  1. trungdung22
    0
    2021-08-02T10:54:04+00:00
    Reply

    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.

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

    Z = \sqrt{20^{2}+10^{2}}

    Z = 22.36 ohm

    V_{rms}=\frac{V_{0}}{\sqrt{2}}

    V_{rms}=\frac{20}{\sqrt{2}} = 14.144 V

    I_{rms}=\frac{V_{rms}}{Z}=\frac{14.144}{\sqrt{22.36}}=0.634 A

    Apparent power is given by

    P = Vrms x Irms

    P = 14.144 x 0.634

    P = 8.97 Watt

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )