LRC Circuits Practice Problems

A partially complete series LRC circuit is constructed from a 200 mH inductor and a 300 µF capacitor. When the resistor is plugged in, the angular frequency decreases by 20%. Determine the resistance that causes the change.

A series LRC circuit contains an inductor, L = 550 mH, a capacitor, C = 0.480 µF, and a resistor R. Determine its angular frequency when its resistor is replaced with a low-resistance wire. 

A series LRC circuit is built from an inductor, L = 0.800 H, and a capacitor, C = 4.00 μF. Determine the resistance of a resistor that will cause critical damping.  

A partially completed series LRC circuit has an inductor, L =  0.400 H, and a capacitor, C = 2.00 μF. Determine the angular frequency of the circuit before a resistor is added to the circuit.

An induction motor operates using 230 V/50Hz electricity. The motor takes in 12 A of electric current and expends electrical energy at a rate of 1000 W. If the power factor of the circuit is to be corrected to 1.0, what capacitor should be used?

Derive an equation for the frequency in a series RLC circuit that causes the greatest energy dissipation. Express the result in terms of ω₀.

Derive an expression for the frequency at which an inductor in a series RLC circuit will experience the greatest potential difference.

A power source with an emf of 9.0 V is used to power a series RLC circuit. If R = 1.5 Ω, L = 1.5 µH and C = 0.5 µF, calculate the potential difference across the inductor when i) ω=ω₀ and ii) ω=ω_L.

The circuit below is used to study current flowing through an inductor. After a sufficiently long time in position a, the switch is moved from a to b at a time t = 0 s. At what value of t does maximum current in the inductor occur?