A series RLC circuit with a resistance of 121.0 Ω has a resonance angular frequency of 5.1 ✕ 105 rad/s. At resonance, the voltages across the resistor and inductor are 60.0 V and 40.0 V, respectively.

At what frequency does the current in the circuit lag the voltage by 45°?

Explanation:

At resonance ω₀L = 1 / ω₀C , L is inductance and C is capacitance .

C = 1 /  ω₀²L , ω₀ = 5.1 x 10⁵ . ( given )

voltage over resistance = R I , R is resistance and I is current

voltage over inductance   =  Iω₀L

R I /  Iω₀L = 60 / 40

R / ω₀L = 3 / 2

L = 2 R / 3 ω₀

= 2 x 121 / 3 x 5.1 x 10⁵

= 15.81 x 10⁻⁵

C = 1 /  ω₀²L

= 1 / (5.1 x 10⁵)² x 15.81 x 10⁻⁵

= .002432 x 10⁻⁵

= 24.32 x 10⁻⁹ F

Let the angular frequency required be ω

Tan 45 = (ωL - 1 / ωC) / R

ωL - 1 / ωC = R

ω²LC - 1 = R ωC

ω²LC = 1 + R ωC

ω² x 15.81 x 10⁻⁵ x 24.32 x 10⁻⁹ = 1 + 121 x ω x 24.32 x 10⁻⁹

ω² x 384.5 x 10⁻¹⁴ = 1 + 2942.72 x10⁻⁹ω

ω² - 7.65 x 10⁶ ω - 1 = 0

ω = 7.65 x 10⁶

frequency = 7.65 x 10⁶ / 2π

= 1.22 x 10⁶ Hz

i dont think you are wrong for wanting to get even with someone who did you wrong.

(i'm an eye for an eye kind of person) but if this person hurt you in a sexual way, i dont suggest doing anything to him. he should be taken to the proper authorities, you could go to jail depending on what you do. if it was something small like your sibling took your spot on the couch, than yea, i would get even with him by taking one of his favorite snacks lol. but i dont suggest you doing anything illegal.

object 2 because all the other ones are wrong