Question

Assuming the passive sign convention and operating frequency of 314 rad/s, calculate the phasor voltage V which appears across each of the following when driven by the phasor current I = 10 mA

a. a 1kΩ resistor.
b. a 1mF capaciotr.
c. a 1nH inductor.

Answer 1

a) 100sin(314t) volts

b) 0.0318sin(314t)

c) 3.14sin(314t) × 10⁻⁹ volt

Step-by-step 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
`X_(c) =(1)/(wc)`

c = 1 × 10⁻³ F

`X_(c) =(1)/(314*1*10^(-3) )` = 3.185 ohms

`V_(m)=IX_(c)` = 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
`X_(L) = wL` =314 × 1 × 10⁻⁹ = 3.14 × 10⁻⁷ ohm

`V_(m)=IX_(L)` = 10 × 10⁻³ × 3.14 × 10⁻⁷ = 3.14 × 10⁻⁹ volt

V(t) = Vmsin(wt) = 3.14 × 10⁻⁹sin(314t) volt =