Answer:
a) 100sin(314t) volts
b) 0.0318sin(314t)
c) 3.14sin(314t) × 10⁻⁹ volt
Explanation:
a) a 1kΩ resistor
w = 314 rad/s
for a resistor, V(t) = Vmsinwt
I = 10 × 10⁻³
R = 10 × 10³ ohms
Vm = IR = 10 × 10⁻³ × 10 × 10³ = 100 V
Therefore V(t) = 100sin(314t) volts
b) a 1mF capacitor
capacitive reactance [tex]X_{c} =\frac{1}{wc}[/tex]
c = 1 × 10⁻³ F
[tex]X_{c} =\frac{1}{314*1*10^{-3} }[/tex] = 3.185 ohms
[tex]V_{m}=IX_{c}[/tex] = 10 × 10⁻³ × 3.185 = 0.0318 volt
V(t) = Vmsin(wt) = 0.0318sin(314t)
c. a 1nH inductor
L = 1 × 10⁻⁹
Inductive reactance [tex]X_{L} = wL[/tex] =314 × 1 × 10⁻⁹ = 3.14 × 10⁻⁷ ohm
[tex]V_{m}=IX_{L}[/tex] = 10 × 10⁻³ × 3.14 × 10⁻⁷ = 3.14 × 10⁻⁹ volt
V(t) = Vmsin(wt) = 3.14 × 10⁻⁹sin(314t) volt =
