Suez Canal University Electric circuits 1 Faculty of Engineering 2nd Level Electrical Engineering Department 1st Semester (2015-2016)

Sheet (6)

Sinusoids and Phasors ================================================================================== (1) A current source in a linear circuit has 𝑖𝑠 = 15 𝑐𝑜𝑠(25𝜋𝑡 − 25°) A

(a) What is the amplitude of the current?

(b) What is the angular frequency?

(c) Find the frequency of the current.

(d) Calculate 𝑖𝑠 at t = 2 ms.

(2) Express the following functions in cosine form: (a) 10 𝑠𝑖𝑛(𝑤𝑡 − 30°). (b) −9 𝑠𝑖𝑛 (8𝑡). (c) −20 𝑠𝑖𝑛(𝑤𝑡 − 45°).

(3) Find the phasors corresponding to the following signals:

(a) 𝑣(𝑡) = 21 𝑐𝑜𝑠(4𝑡 − 15°) 𝑉.

(b) 𝑖(𝑡) = −8 𝑠𝑖𝑛(10𝑡 − 70°) 𝑚𝐴.

(c) 𝑣(𝑡) = 120 𝑠𝑖𝑛(10𝑡 − 50°) 𝑉. (d) 𝑖(𝑡) = −60 𝑐𝑜𝑠(30𝑡 − 10°) 𝑚𝐴.

(4) Obtain the sinusoids corresponding to each of the following phasors:

(5) Simplify the following:

(6) For the circuit shown in Fig. 1, find 𝑍𝑒𝑞 and use that to find current I. Let 𝑤 = 10 𝑟𝑎𝑑/𝑠.

(7) Calculate 𝑣𝑜 (𝑡) in the circuit of Fig. 2.

Figure 1 Figure 2

(8) If the voltage 𝑣𝑜 across the resistor in the circuit of Fig. 3 is 10 cos (2t) V, obtain 𝑖𝑠.

Figure 3

(9) If 𝑖𝑠 = 5 cos(10t - 40°) A in the circuit of Fig. 4, find 𝑖𝑜. (10) Given that 𝑣𝑠(t) = 20 sin(100t - 40°) in Fig. 5, determine 𝑖𝑥 (t).

(11) Determine 𝑣𝑥 in the circuit of Fig. 6. Let 𝑖𝑠 (t) = 5 cos(100t - 40°) A.

Figure 4 Figure 5

Figure 6

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