Question

2. A resistor R and an inductor L are connected in parallel to an AC source...

2. A resistor R and an inductor L are connected in parallel to an AC source providing a voltage v(t) = V sin(ωt).

(a) Draw a phasor diagram showing all the relevant variables of this circuit. You should support your diagram by using Kirchhoff’s rules and what you know about inductors to get full credit. Find the peak value of the total current in terms of V, R, L, and ω.

(b) At an angular frequency, ω0 = 1.0 × 106 rad/s, the resistor and inductor peak currents are equal to each other. What is the inductance L if the resistance is equal to R = 1.7 kΩ?

(c) Find the phase shift between the total current i(t) and v(t) at this frequency.

(d) Write an expression for i(t) at ω = ω0 if V = 220 V. What is the magnetic flux through the inductor when the inductor current is maximum?

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