Question

Use phasor techniques to determine the current supplied by the source given that V = 6 <0o v, R = 7 Ω, C = 12 μF, L = 4 mH and ω = 2000 rad/sec. The current supplied by the source is I = ∠ ° A

Answer 1

Given Information:

Voltage = V = 6 < 0° V

Resistance = R = 7 Ω

Capacitance = C = 12 μF

Inductance = L = 4 mH

Frequency = ω = 2000 rad/sec

Required Information:

Current = I = ?

Answer:

I = 0.174 <78.25° A

Step-by-step explanation:

The current can be found using

I = V/Z

Where Z is the impedance an can be calculated as

Z = R + J(XL - XC)

Where XL is inductive reactance and XC is capacitive reactance

XL = ω*L

XL = 2000*0.004

XL = 8 Ω

XC = 1/ω*C

XC = 1/2000*12x10⁻⁶

XC = 41.66 Ω

So the impedance can be calculated now

Z = R + J(XL - XC)

Z = 7 + J(8 - 41.66)

Z = 7 - J33.66 Ω

|Z| = √(7²) + (-33.66)²

|Z| = 34.38 Ω

Magnitude of the current

I = V/|Z|

I = 6/34.38

I = 0.174 A

Magnitude and angle both

I = 6 < 0°/(7 - J33.66)

I = 0.0355 + j0.1708 A

in the polar form

I = 0.174 <78.25° A