Question

A resistor R = 1 kohm an inductor L = 1 mH and a capacitor C = 1 muFare used in a circuit which is driven by a voltage source v_s(t) = 10 sin(10^5 t + 45degree)(waming: note the input is a sine function not a cosine function.) What is the phasor corresponding to the voltage source? Express it in the polar form AZB and write your answer as "A B" without the quotation marks.

Answer 1

A = 10, B = -45

Step-by-step explanation:

Given a voltage source of the form
`A\cos(\omega t + \phi)` the correspondent phasor is of the form
`A\angle \phi`. Note that the phasor form is only considered for sources expressed in a cosine form. IN this case, since the question is only asking for the phasor of the voltage form, the way the other devices are connected is neglected and do not affect the answer. Then, to get the phasor of the voltage source, we need to express it in a cosine form. To do so, the following trigonometric equation is used
`\sin(\omega t + \phi) = \cos (\omega t +\phi - 90^\circ)`

Therefore, the voltage source, in terms of cosine, is equivalent to
`10 \cos(10^5 t +45^\circ- 90^\circ)= 10 \cos(10^5 t -45 ^\circ )`, so the correspondent phasor form is
`10\angle -45`.