The first is a series connection of a sinusoidal voltage source vs(t)= 0.5cos(ωt), a single resistor of value R and a single capacitor of value C. The second circuit is a series connection of a sinusoidal voltage source of the same value as above, a single resistor of value R and a single inductor of value L.
If the resistor voltage (in both circuits), the capacitor voltage and the inductor voltage must have the same magnitude, find the required relationships between R, L, C and ω.
Hints: Combine the impedances and find phasor current in the two circuits by using Phasor Ohm ( I= V/Z), then find voltage across each element (eg: VR = I * ZR ). Setting magnitudes equal is the same as setting the square of the magnitudes equal. Which can be obtained by multiplying the expression by its complex conjugate.