Question

If an R = 1-kΩ resistor, a C = 1-μF capacitor, and an L = 0.2-H inductor are connected in series with a V = 150 sin (377t) volts source, what is the maximum current delivered by the source?

Answer 1

given,

R = 1-kΩ = 1000 Ω

C = 1-μF

L = 0.2-H

V = V_max sin( ω t)

comparing

V = 150 sin ( 377 t)

ω = 377

`\chi_c = (1)/(\omega C)`

`\chi_c = (1)/(377 * 1 * 10^(-6))`

`\chi_c = 2652.5\Omega`

`\chi_L =377 * 0.2`

`\chi_L =75.4\ \Omega`

Impedance,

`Z = √(R^2+(\chi_L-\chi_c)^2)`

`Z = √(1000^2+(75.4 -2652.5)^2)`

Z = 2764.3 Ω

now,

V_{max} = 150 V

`I_(max) = (V)/(Z)`

`I_(max) = (150)/(2764.3)`

`I_(max) = 0.0543`

`I_(max) = 54.3\ mA`