Question

In the adjoining circuit schematic, in steady-state, the current flowing through the loop causes a voltage drop across the resistor, having the waveform

vR(t) = 15 cos (75 t) and a voltage drop across the capacitor given by vC(t) = 20 cos (75 t + 90⁰)

(a) Express the above two voltages in phasor form. (b) Find the source voltage shown in the circuit schematic, expressed in phasor form. (c) Express the source voltage v(t) as a function of time.

250 Ω M- ν(ε) 40 μF

Answer 1

Consider the circuit given 2500 Ult) a your Given VRIE) = 15 Cos (756); Velt) = 20001765+90°) To write the polar form consider an example = A COUCwtt In polar form it'll be ALO - Now for URIt) = 15 cod febt + 0°) = 15L0° for VC (t) = 20 cos (45+ +900) 20 1900 we have to convert this into rectangellan for and the Add these two voltage to get the vit) consider loop Equation UR U(t)= Voltst velt) = 15L0° + 20490 UCL) - 15+920 This is in Rectangular foron for suppose, atſb to get in polage form va+62 ftan"(bl) 2 Don + * Vit) Vc ai Vit) = 25 53.130 Vit) = 25 cos (75t+53113)