Question

In the circuit below, assume that 1,0) = (1 mA) cos25x 105) cos(107t). Find v (t). i (t) 10 uH 1000 pF Hint: from trigonometry, cos(a + b) = cos(a) cos(b)-sin(a) sin(b) cos(a-b) = cos(a) cos(b) + sin(a) sin(b) Adding these two equations removes the sin terms, giving cos(a + b) + cos(a-b) = 2 cos(a) cos(b) Therefore, a signal that is the product of two cosine waveforms at given frequen- cies can be represented as the sum of two cosines at the sum and difference of these given frequencies.
Ans =sqrt(2)cos(10^7t)cos(2.5*10^5t-pi/4)

Plz show all the steps

Answer 1

İ;㈩ニ using 1汝9二 1.goos(45x",ft) (勿(tat acos a co b=Cの(a + b) + co (a-b) ㄧ s|CoS@+25x159 +cos [(7-25치애 Giver, R. Apply kcL at no de 2000 S

VoCs) 치 this is tanster funchan be Ve and i Nao , becausea.p siousbida l cumeu:トリノWe. 2 at to= 102-5X/00 253ux +8.6265 x@s 1 4 7.2 x lo12 二 102-5X10 225.25

2 simil. because o+ +)-10?cos (99.5x179 2 H(o) 992 x 1014 6.939メ1012 44.63。 V15 2 v,2버드 0Ro275 Cos (cr7.5x105t + 44. 6s')._-9 ③

(u2t +44.63) ut O 63 - Sinust si 44-63

Vi Cの@jt-Th) + ('co@ftma) 0.5+ Vī 2