Answer:
a.1127.7Ω
b.0.1714A
c.[tex]0.9^{0}[/tex]
Explanation:
From our knowledge of AC Circuit, where we have the resistor arranges in series with the capacitor, the total impedance(Z) of the circuit is given as
[tex]Z=\sqrt{R^{2}+X_{C} ^{2}}\\[/tex]
Where R is the resistor value in the circuit and [tex]X_{C}[/tex] is the circuit capacitance due to the capacitor in the circuit and is express as
[tex]X_{C}=\frac{1}{WC}\\[/tex]
By inserting values, we can determine the value of the capacitance
[tex]X_{C}=\frac{1}{120\pi *3*10^{-6}}\\X_{C}=884.19\\[/tex]
since the resistor value is 700Ω, we can substitute into the equation for the impedance
[tex]Z=\sqrt{700^{2}+884.19 ^{2}}\\Z=1127.7ohms\\[/tex]
b. from the expression of Ohms law, [tex]V=IR[/tex]
the voltage in this case is the amplitude of the voltage in the question i.e 120v
Hence [tex]I_{R}=120/700\\ I_{R}=0.1714A\\[/tex]
C. the phasor angle is express as
[tex]tan\alpha=\frac{X_{C} }{R}[/tex]
[tex]tan\alpha=\frac{884.19 }{700}\\tan\alpha=1.263\\\alpha=tan^{-1}(1.263)\\\alpha =0.90\\[/tex]
Answer:
a) 1127.7ohms
b) 0.1714A
C) 0.90°
Explanation:
From the AC Circuit where resistor and capacitor are arrange in series
Z=√(R)²+(XC)², Where R= resistor, Xc= Capacitance, also Xc=1/Wc
Therefore Xc= 1/120π×3×10⁻6, ∴ Xc= 884.19
Using Resistor R= 700ohms
Impedance Z= √(700)²+(884.19)² = 1127.7ohms
b) Using V=IR, and Voltage V= 120V
Hence Current I=V/R= 120/700= 0.1714A
c) The phase angle is express as TanФ=Xc/R =884.19/700= 1.263
Ф=Tan⁻⁽1.263⁾ =0.90°
