A voltage v(t) = 100 cos(60t + 20°) V is applied to a parallel combination of a 40-kΩ resistor and a 50-μF capacitor. Find the steady-state

Question

A voltage v(t) = 100 cos(60t + 20°) V is applied to a parallel combination of a 40-kΩ resistor and a 50-μF capacitor. Find the steady-state currents through the resistor and the capacitor.

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Vodka 5 years 2021-09-05T12:22:38+00:00 1 Answers 15 views 0

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  1. linhdan
    0
    2021-09-05T12:24:06+00:00
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    Answer:

    Current through resistor i_{r}=2.5cos(60t+20)mA

    Current through capacitor i_{c}=-0.3sin(60t+20)A

    Explanation:

    Given data

    Voltage v(t) = 100 cos(60t + 20°) V

    Resistance R=40-kΩ

    Capacitor C=50-μF

    To find

    Steady-state currents through the resistor and the capacitor.

    Solution

    The current flows through the resistor is:

    i_{r}=\frac{v(t)}{R}\\ i_{r}=\frac{100cos(60t+20)}{40*10^{3} }\\ i_{r}=2.5cos(60t+20)mA

    Now the current flows through capacitor is:

    i_{c}=C\frac{dv(t)}{dt}\\ i_{c}=50*10^{-6}(\frac{d(100cos(60t+20))}{dt})\\ i_{c}=50*10^{-6}*100(-60)sin(60t+20)\\ i_{c}=-0.3sin(60t+20)A

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