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9 December, 12:30

Find the equivalent impedance Zeq seen by the source when Vs = 4 cos (4t) v, C = 0.5 F, R = 1 Ω and L = 0.5 H. (Give angles in degrees and round final answers to two decimal places.) Calculate the voltage across the capacitor. (Give angles in degrees and round final answers to two decimal places.)

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  1. 9 December, 15:53
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    Zeq = 1.80ohms

    Vc = 1.11cos4t volts

    Explanation:

    Impedance of an AC circuit is defined as the opposition to the flow of current across the resistor, capacitor and inductor of an AC circuit. It is expressed mathematically as;

    Zeq = √R² + (Xl-Xc) ²

    Where R is the resistance

    Xl is the inductive reactance

    Xc is the capacitive reactance

    Xl = 2πfL

    Source voltage Vs = Vcos2πft

    Given Vs = 4 cos (4t) v

    Comparing both source voltage to get the frequency f, we have;

    2πft = 4t

    2πf = 4 ... (1)

    Given L = 0.5H

    C = 0.5F

    R = 1.0ohms

    Xl = 4*0.5 (note that 2πf = 4 from equation 1)

    Xl = 2.0ohms

    Xc = 1/2πfC

    Xc = 1/4 (0.5)

    Xc = 1/2

    Xc = 0.5ohms

    To get the impedance Z

    Zeq = √1² + (2-0.5) ²

    Zeq = √1+1.5²

    Zeq = √3.25

    Zeq = 1.80ohms

    The voltage across the capacitor is expressed as Vc = IXc

    Since we know Xc = 0.5ohms

    We need current I

    To get current we use the relationship Vs = IZ

    I = Vs/Z =

    4 cos (4t) / 1.8

    I = 2.22cos4t A

    Vc = 2.22cos4t * 0.5

    Vc = 1.11cos4t volts
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